Student Solutions () - Math-U-See 2 sYstEMAtic REVi EW 1D - sY stEMAtic REVi EW 1E 254 soLUtions 1...
244
ALGEBRA 2 251 LESSON PRACTICE 1A - LESSON PRACTICE 1B ALGEBRA 2 251 STUDENT SOLUTIONS Student Solutions Lesson Practice 1A 1. 2. 3. 3 1 3 1 9 1 1 2 2 2 1 1 − − = = = = − X X X ( 3 2 3 4 9 1 2 2 1 2 8 1 1 1 2 2 2 2 3 3 3 5 5 5 ) () =− = = = = = = − − 4. 5. 6. X X X 3 3 3 2 6 3 263 11 4 1 2 1 8 2 2 2 2 2 2 048 = = ⋅ ⋅ = = ⋅ ⋅ + + 7. 8. , or RR R R R X X X X X or 2 142 7 1 3 4 13 4 2 1 = = ⋅ ⋅ = = + + − − − ( ) ++− ( ) − 9. X X A B AB 2 0 2 2 0 2 2 0 3 3 3 4 4 4 4 4 1 10. 11. 12. ⋅ = ⋅ ⋅ = = = + − +− ( ) + A A B A AB AB X X X X or ⋅ ⋅ = = = = = + + + − − 2 2 3 2 6 26 4 4 5 5 5 5 1 5 13. ÷ 1 625 2 2 2 2 1 2 3 0 30 3 4 2 4 2 2 14. 15. Y ÷Y Y Y = = = = = − − − −−− ( ) − 2 16 7 16 7 9 2 4 24 6 1 4 or X X X X B B B B o 16. 17. ÷ ÷ = = = = − − −− − r B Y Y Y Y or Y X X X 1 1 6 4 8 48 4 4 3 4 34 12 18. 19. 2 = = ( ) = = − − ⋅ 0. 21. 5 5 5 1 0 3 03 0 2 2 3 223 12 ( ) = = = ( ) ( ) = = ⋅ ⋅⋅ A A A 22. 33 AB A B AABB A B AB or A B H − − + +− ( ) − − = = = 24 323 4 323 4 5 1 5 4 23. N HN HHNN H N H N or N 6 12 4 16 2 4 1 6 2 54 4 = = = − − − −+− ( ) +− ( ) − H P QP QQP P PP QQQ P 5 2 03 164 23 4 0 1 6 23 4 24. − − − − − −++− ( ) = = Q P Q or PQ 01 6 3 5 35 1 ++− ( ) − − = Lesson Practice 1B 1. 2. 3. 4 1 4 1 64 7 343 1 3 3 3 − = = − or ( − = − − = − − = = = = = − − 3 1 3 1 27 1 27 1 1 1 3 3 1 9 1 3 3 3 1 1 2 2 ) 4. 5. A A A = = = ⋅ ⋅ = = + + 9 1 3 1 3 1 9 33 3 3 3 243 2 2 2 1 0 4 104 5 6. 7. 8. () or X X X X X Y Y Y Y or 2 3 10 2 3 10 9 6 0 60 6 ⋅ ⋅ = = ⋅ = = − +− ( ) + − −+ − 9. 1 2 2 2 6 6 6 6 6 6 3 3 4 2 5 1 42 51 Y A B A B 10. 11. ⋅ = ⋅ ⋅ ⋅ = + − ++− ( ) + = = ⋅ = = = = = − +− ( ) − − 6 36 1 2 9 9 9 9 0 2 3 23 1 12. 13. A A A A B ÷B B B or B X X X X 1 0 8 0 8 8 14. ÷ − −− ( ) = = Solutions are shown in detail. The student may use canceling and other shortcuts as long as the answers match. If you see an error, see online solutions mentioned on page 14.
Transcript of Student Solutions () - Math-U-See 2 sYstEMAtic REVi EW 1D - sY stEMAtic REVi EW 1E 254 soLUtions 1...
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ALGEBRA 2 251LEsson PRActicE 1A - LEsson PRActicE 1BALGEBRA 2 251
stUDEnt soLUtions
Student SolutionsLesson Practice 1ALesson Practice1A1.2.
3.
3 1
3
19
1 1
2
22
11
= =
= =
XX X
( 33 2349
1
2
21
2 8
11
12
2 2
2
3
33
5
55
)
( )
= =
= = =
= =
4.
5.
6.
X
X X
33 3
3
2 6 3 2 6 3 11
4
1
2
18
2 2 2 2 2 2 048
= =
= =
+ +7.
8.
,or
R R RR R R
X X X
X X or
2 1 4 2 7
1 3 4
1 3 4 2 1
= =
=
=
+ +
( )+ + ( )
9.
XX
X
A B A B
2
0 2 2 0 2 2 0
3 3 3
4 4 4 4 4 1
10.
11.
12.
=
= = =
+
+ ( )+
AA A B A A B A BX X X X
or
= =
= = =
+ + +
2 2 3
2 6 2 6 44
5 5 5 5 1
513. 1
625
2
22 2 1
2
3 0 3 0 3
4
24 2 2
14.
15.
Y Y Y Y= =
= = =
( )
22
16 7 16 7 9
2 4 2 4 6
14
or
X X X X
B B B B o
16.
17.
= =
= =
rrB
Y
YY Y or
Y
X X X
1
1
6
4
84 8 4
4
34
34 12
18.
19.
2
= =
( ) = =
00.
21.
22.
5 5 5 103
03 0
22
3223 12
3 3
( ) = = =
( )( ) = =
A A A
A B
AA BA A B B
A B A B or AB
H
+ + ( )
= =
=
2 43 2 3 4
3 2 3 4 5 15
423. nn
HnH H n n
H n H n or n
6
1 24 1 6 2
4 1 6 2 5 44
= =
=
+ ( ) + ( ) HH
P Q P
Q Q PP P P Q Q Q
P
5
2 0 3
1 6 42 3 4 0 1 6
2 3 4
24.
+ + ( )
= =
( )
1625
2
22 2 1
2
3 0 3 0 3
4
24 2 2
14.
15.
= =
= = =
( )
22
16 7 16 7 9
2 4 2 4 6
14
or
X X X X
B B B B o
16.
17.
= =
= =
rrB
Y
YY Y or
Y
X X X
1
1
6
4
84 8 4
4
34
34 12
18.
19.
2
= =
( ) = =
00.
21.
22.
5 5 5 103
03 0
22
3223 12
3 3
( ) = = =
( )( ) = =
A A A
A B
AA BA A B B
A B A B or AB
H
+ + ( )
= =
=
2 43 2 3 4
3 2 3 4 5 15
423. nn
HnH H n n
H n H n or n
6
1 24 1 6 2
4 1 6 2 5 44
= =
=
+ ( ) + ( ) HH
P Q P
Q Q PP P P Q Q Q
P
5
2 0 3
1 6 42 3 4 0 1 6
2 3 4
24.
+ + ( )
= =
QQ P Q orP Q
0 1 6 3 53 51+ + ( ) =
Lesson Practice 1BLesson Practice1B1.
2.
3.
4 1
4
164
7 343
1
33
3
=
=
or
( = =
=
= =
= =
31
3
127
127
11
1
3
31
91
3 3
3
1
1
2
2
)4.
5.
A
A A
==
= =
= =+ +
9
13
1
3
19
3 3 3 3 3 243
2 2
2
1 0 4 1 0 4 5
6.
7.
8.
( )or
XX X X X X
Y Y Y Y or
2 3 10 2 3 10 9
6 0 6 0 6
= =
= =
+ ( )+
+ 9. 1
2 2 2
6 6 6 6 6
6
3 3
4 2 5 1 4 2 5 1
YA B A B10.
11.
=
=
+
+ + ( )+ == =
= = =
= =
+ ( )
6 36
1
2
9 9 9 9 0
2 3 2 3 1
12.
13.
A A A A
B B B B oorB
X X X X
1
3
33 3 1
3
0 8 0 8 8
2
32 3 1
14.
15.
16
( )
= =
= = =
..
17.
18.
6 6 6 616 12 16 12 4
4
A B B A B B A
Y Y Y Y
A
+ +( )
= =
= =
AAA A or
A
Y Y Y o
54 5 9
9
210
2 10 20
1= =
( ) = =
( ) ( ) 19. rrY
Z Z
1
8 8 8 1
20
20
2 0 0
32
53 2
20.
21.
( ) = = =
( )( )( )
Solutions are shown in detail. The student may use canceling and other shortcuts as long as the answers match. If you see an error, see online solutions mentioned on page 14.
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ALGEBRA 2
LEsson PRActicE 1B - sYstEMAtic REViEW 1c
soLUtions252
1
2 2 2
6 6 6 6 6
6
3 3
4 2 5 1 4 2 5 1
YA B A B10.
11.
=
=
+
+ + ( )+ == =
= = =
= =
+ ( )
6 36
1
2
9 9 9 9 0
2 3 2 3 1
12.
13.
A A A A
B B B B oorB
X X X X
1
3
33 3 1
3
0 8 0 8 8
2
32 3 1
14.
15.
16
( )
= =
= = =
..
17.
18.
6 6 6 616 12 16 12 4
4
A B B A B B A
Y Y Y Y
A
+ +( )
= =
= =
AAA A or
A
Y Y Y o
54 5 9
9
210
2 10 20
1= =
( ) = =
( ) ( ) 19. rrY
Z Z
1
8 8 8 1
20
20
2 0 0
32
53 2
20.
21.
( ) = = =
( )( ) =
( )( )
( ) (( )( )
+
=
= =
5 3030
2 2
4 52 4 2 5
2
1Z orZ
X Y
X YX X Y Y
X
22.
44 2 5 6 3
2 2
2
3
333 3
3 3
3
3
3
33
Y X YA A
B
A A
B B
A
BA
+
+
+
=
= = =23.2B
33
3 3
3
3 3 3 3
5 3 2
1 6 35 6 3
+ ( )
=
=
=
B
A B A B
R s s
sR RR R R24. ss s s
R s R s orR s
+ ( )+ ( ) + + ( )
=
=
3 2 1
5 6 3 3 2 1 4 241
22
Systematic Review 1CSystematic Review 1C1.
2.
5 1
5
125
4 4 4
22
5 2 4
=
or
== =
=
=
+ + ( )
4 4 64
31 5 26
5 2 4 3
0 0( ) ( )
or
X X XA B A B3.
4.
==
( ) =
( )( ) = ( ) = ( ) ==
( )( )
1
2 2 2
2
32
3 2 6
6 6
5.
6.
Y Y
A A A
A
DG
DG
664 6
4 3
0 54 0 5 3 4 0 5 3
9 3
A
X Y
X XX X X Y X Y
X Y or
7.
+ +
= = =
XX
Y
9
3
8. X Y Y X
X YX X X Y Y Y
X Y
+ + + +
= =3 4 2
5 23 1 5 4 2 2
3 1 5 4 2 22 3 43
4
214 14 14 196
15
( ) =
= ( )( ) =
( )
X Y or X
Y
9.
10.22
15 15 225= ( ) ( ) =11. given
12. 1 1 086 2 4
1 000 1 1 1 000 086 1 000 2
. . .
, . , . ,
=
( ) ( ) = ( )B
..
, ,
, ,
,,
4
1 100 86 2 400
1 014 2 400
1 0142 400
1694
B
B
B
B
=
=
=
000= B
13. 3 2 15
12
310
5 15
12
310
265
12
310
101
265
+ =
=
=
M
M
M
( )( )) ( )( ) ( )( )= =
=
101
12
101
310
2605
102
3010
52 5 355
M
M
M==
= =
= +
( ) = ( )
5555
11
388 1 3 3
1 000 388 1 000 1
M
M
Q14. . . .
, . , .. , .
,
3 1 000 3
388 1 300 300
912 300
912300
+ ( )= +
=
= =
Q
Q
Q
Q
= ( )
+ =
3 125
12 6 6 2
15 18 21
3
2
3 2
15.
16.
A AB A A B
AB BA B
B 55 6 7
13 2 4 13 26 52
2
2 2
2
AB A B
X X X X
X X
+ ( ) +( ) = + 17.
18. YY X X Y X
+( ) = + +( ) = +
3 3 5
2 2 215 6 8 2 4 9 10
15 6 64 2
19.
4 81 100
15 6 32 4 19
15 6 8 19
9 8
( ) = +( ) = +( ) =
+( ) 11917 19 323
4 8 5 2 3 6 7 9
32 5 2
2 2
2
=( ) =
+( ) =
+( )
20.
=
+( ) =
3 6 49 9
27 2 3 6 441
29 3 441
841 44
2
2
-
ALGEBRA 2
sYstEMAtic REViEW 1c - sYstEMAtic REViEW 1D
soLUtions 253
. . .
, . , .. , .
,
3 1 000 3
388 1 300 300
912 300
912300
= ( )
+ =
3 125
12 6 6 2
15 18 21
3
2
3 2
15.
16.
A AB A A B
AB BA B
B 55 6 7
13 2 4 13 26 52
2
2 2
2
AB A B
X X X X
X X
+ ( ) +( ) = + 17.
18. YY X X Y X
+( ) = + +( ) = +
3 3 5
2 2 215 6 8 2 4 9 10
15 6 64 2
19.
4 81 100
15 6 32 4 19
15 6 8 19
9 8
( ) = +( ) = +( ) =
+( ) 11917 19 323
4 8 5 2 3 6 7 9
32 5 2
2 2
2
=( ) =
+( ) =
+( )
20.
=
+( ) =
( ) =
3 6 49 9
27 2 3 6 441
29 3 441
841 44
2
2
44
841 444 397
=
=
Systematic Review 1DSystematic Review 1D1.
2.
3.
X0
44
2
1
2 1
2
116
5 5
=
= =
66 2 6 88
9 3 9 3 6
75
7
5 5 1
5
9 9 9 9
8 8
= =
= =
( ) =
+ ( )
or
4.
5.
(( )( )
( )( )
=
( ) = = =
5 35
20
2 0 0
2 2 4 3 2 1
8
9 9 9 1
3
6.
7. M n M M n == = + ( )+ ( ) +
3
9 9
2 2 3 2 4 1
7 55
7
6 4
M n
M n or n
M
R RP
P8.
99 46 1 4 4 9
6 1 4 4 9 1 13
RR R R P P
R P R P or
+ + + ( )
= =
= 11
1 15
65
6
5
3625
1 1125
13
2 2 2
2
RP
9.
10.
( ) ( ) = =
=
=
( )
( )
= ( )( )( ) = 2 2 2 2 83
11. 34
56
710
60 34
60 56
60 710
1804
3006
4
=
( ) ( ) = ( )
=
R
R
R 22010
45 50 42
50 3
350
350
5 3 002
1
=
=
=
=
+ =
R
R
R
Y12. . . .
,, . , . , .000 5 1 000 3 1 000 002
500 300 2
500
( ) + ( ) = ( )+ =
=
Y
Y
Y
= =
298
298500
149250
Y
13. 3 23
512
1 14
113
512
54
12 113
12 512
12
=
=
( ) ( ) = ( )
K
K
K 554
1323
6012
604
44 5 15
5 29
295
5 45
1
=
=
=
=
=
K
K
K
K
14. .. . .
, . , .
, .
203 9 6
1 000 1 203 1 000 9
1 000 6
H
H
+ =
( ) + ( ) =( ) (( )
+ =
=
= =
1 203 900 600
1 203 1500
15001203
1 297
,
,
H
H
H11203
1 99401
56 49 28
7 8 7 4
4 1
2
=
( )
15.
16.
X XA X
X A X
X 66
4 1 4
2 5 3 8 40 24
3
2
3 2 4 3 5
X
X X
X X X X X X
or
=
( )( ) +( ) = +17.
is customary to put equation
24 8 405 4 3X X X
it
+
ss in
order by value of the exponents.reverse
188. 5 3 4
15 20 5
5
2 2 3
3 3 2 4 4
4
X Y X YX X Y
X Y X Y X Y
or X Y
+ ( ) =+
44 3 2 3
2
2
20 15
10 3 9 20
13 9 20
1
+ +
+( ) ( ) =( ) ( ) =
X Y X Y
19.
669 9 20
160 20 8
42 6 2 11 13
7 2 1
2
( ) =( ) =
[ ] =[ ]
20.
11 169
5 11 169
55 169 114
=
-
ALGEBRA 2
sYstEMAtic REViEW 1D - sYstEMAtic REViEW 1E
soLUtions254
1 203 900 600
1 203 1500
15001203
1 297
,
,
H
H
H11203
1 99401
56 49 28
7 8 7 4
4 1
15.
16.
X XA X
X A X
X 66
4 1 4
2 5 3 8 40 24
3
2
3 2 4 3 5
X
X X
X X X X X X
or
=
( )( ) +( ) = +17.
is customary to put equation
24 8 405 4 3X X X
it
+
ss in
order by value of the exponents.reverse
188. 5 3 4
15 20 5
5
2 2 3
3 3 2 4 4
4
X Y X YX X Y
X Y X Y X Y
or X Y
+ ( ) =+
44 3 2 3
2
2
20 15
10 3 9 20
13 9 20
1
+ +
+( ) ( ) =( ) ( ) =
X Y X Y
19.
669 9 20
160 20 8
42 6 2 11 13
7 2 1
2
( ) =( ) =
[ ] =[ ]
20.
11 169
5 11 169
55 169 114
=
[ ] = =
Systematic Review 1ESystematic Review 1E
1.
2.
( )13 1319
10 10
2 2
2
24
= =
( ) =
22 4 88
0 1
10 1
10
4 4 4
11 11 11 1
( ) ( )
+
=
=
=
or
A B A B3.
4. 11 11 11 11
3 3
5 5 5
0 1 0 1
44
32
3 2 6
= = =
( ) =( ) = =
( )( )
5.
6.
7.
D D
BB B c
B cB B B c c
B c B c o
5 2 5
4 35 2 4 5 3
5 2 4 5 3 11 2
+ + +
= =
= rr B
c
D c D
D c cD D D c c c
c
11
2
6 4 2
4 0 26 2 4 4 0 2
4 0
8.
+ +
= =
22 6 2 4 6 1212
6
2 2 22 3
4114
11
( ) + + =
= =
D c D or D
c
9. ( ) ( )44
12116
7 916
10 10 000
2
4
= =
( ) =10. ,
11. =
=
( ) + ( )
5 12
29
518
112
29
518
18 112
18 29
Y
Y
Y( ) ( )) ( )= ( ) =
=
=
=
18 518
1982
369
9018
99 4 5
99 9
999
Y
Y
Y
Y ==
+ =
( ) ( ) + ( )( ) = ( )
111
7 8 1 2
10 7 10 8 10 1
12. . . .
. .
A A
A A ..2
7 8 12
12
( ) + =
=
A A
A
13. 1 23
2 14
135
53
94
85
60 53
60 94
60
= +
= +
( ) = ( ) +
A
A
( ) ( ) (( )= +
= +
=
( )85300
3540
44805
100 135 96
235 96
2359
A
A
A
A
662 43
963 1 6 34
100 3 100 1 6 100
= =
=
( )( ) ( )( ) =
A
X
X
14. . .
. (( )( ) =
=
= =
.34
300 160 34
300 194
194300
97150
9
X
X
X
M15. 110 19 9 10 19
36 72 45 9
3 2 2
2 2
M M M M M
M M M M
+ = ( ) +( ) + = (16. )) +( ) =( ) ( ) ( ) +( )
4 8 5
9 4 3 9 4 33 1
M M
M M M M
A XA
or
17. ++ ( ) =+
+( ) =
2
2
4 2
2 1 2
4 2 4 5
1 1 2 1 1 1
X A A
XA X A A
A B A A B B18.
AA B A B AB3 2 2 2
2 2
4 2
19 7 2 6 19 14 6
19
+
( ) ( ) + = + =
19.
+ = + =
+ =
+ + =
+
14 6 19 14 36
33 36 3
5 3 7 7 8 4
5 3
2
220.
77 7 2
5 3 7 7 2 5 3 49 7 2
15 49 7 2 64 7 2
2
2
+ =
+ + = + + =
+ + = + == + =57 2 59
-
ALGEBRA 2
sYstEMAtic REViEW 1E - LEsson PRActicE 2B
soLUtions 255
=
+
+( ) =
2
2
4 2
2 1 2
4 2 4 5
1 1 2 1 1 1
X A A
XA X A A
A B A A B B18.
AA B A B AB3 2 2 2
2 2
4 2
19 7 2 6 19 14 6
19
+
( ) ( ) + = + =
19.
+ = + =
+ =
+ + =
+
14 6 19 14 36
33 36 3
5 3 7 7 8 4
5 3
2
220.
77 7 2
5 3 7 7 2 5 3 49 7 2
15 49 7 2 64 7 2
2
2
+ =
+ + = + + =
+ + = + == + =57 2 59
Lesson Practice 2ALesson Practice 2A1.
2.
3.
correct
correct
incorrect:: X2 + +
+ +=
+ ++
+ ++
+ +
3 6
2 7
2 7
3
2 7
6
2 7
2
2
2 2 2
X
X X
X
X X
X
X X X X
4..
5.
incorrect: BB
+ = + =
+ =( ) +( ) = +
B
X XX
X XX
X
0
2
1 1 2
4 4 1 4 111
4 1
2 2 21
2
4 42
4
2
= +
+ =( ) +( ) = + = +
+ =( )
X
Y YY
Y YY
Y Y
X Y X
6.
7. ++( )
= +( )
=
+( ) ++ =
(
Y X Y
X Y or X Y
AB AA
A
22
12 2 2
12 164
428.)) +( ) = +
+ =( ) +( )
( )
3 44
3 4
5 205
5 45
B AA
B A
XY XYZYZ
Y X XZY
9.ZZ
X XZZ( )
= + 4
this fraction cannot be reduced
furthher because Z cannot be factored
out of the nummerator.
10.
1
2 2
21
2
2 2X Y XYXY
XY X YXY
X Y X Y
=( ) ( ) =
=
11.
12.
62
42
6 42
34
3 34
3 44
XX
XX
X
XXX X
++
+= +
+
+ =( )( ) +
( )( ) ==
+ = +
=( )( )
( )
34
124
3 124
74
34
74
34
XX X
XX
X YY
X YX
Y X13. (( ) =
=( )( )
( )( ) =
7 34
2 2
Y XXY
AB
BA
A AB A
B BA B
A BAB
14.
155. 31
21
3 11 1
2 11
XY
XY
X YY Y
X YY Y
+
+=
+( )( ) +( )
+ ( )
+( ) 113 1 2 1
1 13 3 2 2
1
( ) =
+( ) + ( )+( ) ( )
=
+ + +
X Y X YY Y
XY X XY XY(( ) ( )
= ++( ) ( )
+ = +
YXY X
Y Y
orY Y
XY1
51 1
1
5: 5XY+X
Y2XX
YRt
RsRt
Rt
st
R st
2 1
+ = + = +16.
11.
12.
62
42
6 42
34
3 34
3 44
XX
XX
X
XXX X
++
+= +
+
+ =( )( ) +
( )( ) ==
+ = +
=( )( )
( )
34
124
3 124
74
34
74
34
XX X
XX
X YY
X YX
Y X13. (( ) =
=( )( )
( )( ) =
7 34
2 2
Y XXY
AB
BA
A AB A
B BA B
A BAB
14.
155. 31
21
3 11 1
2 11
XY
XY
X YY Y
X YY Y
+
+=
+( )( ) +( )
+ ( )
+( ) 113 1 2 1
1 13 3 2 2
1
( ) =
+( ) + ( )+( ) ( )
=
+ + +
X Y X YY Y
XY X XY XY(( ) ( )
= ++( ) ( )
+ = +
YXY X
Y Y
orY Y
XY1
51 1
1
5: 5XY+X
Y2XX
YRt
RsRt
Rt
st
R st
2 1
+ = + = +16.
Lesson Practice 2BLesson Practice 2B1. incorrect:
3X+1
+
=
( )
61
3 1X
XXX X
XX X
X XX
+( ) ( )+ +
( )( ) +( )
=
( ) + +( )( )
1 16 1
1 1
3 3 6 61 XX
XX X
or X
X
+( )=
+( ) +( )
+
19 31 1
9 3
12
2. incorrect: 144
correct
correct
+ = + =
+ =( )
24
1 24
34
4 2
2
2 2
3.
4.
5. Y Y
Y
Y Y ++( ) = + = +
+ + =( ) + +( ) =
+
1 11
1
6 3 33
3 23
2
2
22
Y
Y Y
X A X X A X
X A
6.
++ = + + = +
+ =( ) +( )
X X A X X A
X Y X YXY
XY X XX
12 3
16 82
2 8 42
3 2 27.
YY
X X X X
A B c ABcAB
A
=
+ = +
=
8 41
8 42
2
2 3 4 2
or 4X(2X +1)
8.BBc AB c
AB
c AB c or AB c c
R
2 2 2
2 2 2 2 4 2
1
1
2 2
( ) ( )=
( ) +9.
RRR
R
X AA
X A
+( )= +
( )+( )
= =
=( ) ( )
12 1
121
2
5 55
52 2 2 210.(55
82
12
8 22 2
1 2
2 2
)AX A
A
X XX
X XX
=
++
=
( )+( ) ( )
+ +
11.
(( )( ) +( )
=
( ) +( )+( ) ( )
=
X X
X XX X
X X
2 2
8 2 1 22 2
8 16 2XX X
XX X
or X
X
+( ) ( )=
+( ) ( )
+
2 27 18
2 27 18
412
6
2
12.AAB
ABAB AB
ABAB
A BB
=( )( ) +
( )( ) =
+
=
12
6 22
122
82
32
8
-
ALGEBRA 2
LEsson PRActicE 2B - sYstEMAtic REViEW 2c
soLUtions256
YY
X X X X
A B c ABcAB
A
=
+ = +
=
8 41
8 42
2
2 3 4 2
or 4X(2X +1)
8.BBc AB c
AB
c AB c or AB c c
R
2 2 2
2 2 2 2 4 2
1
1
2 2
( ) ( )=
( ) +9.
RRR
R
X AA
X A
+( )= +
( )+( )
= =
=( ) ( )
12 1
121
2
5 55
52 2 2 210.(55
82
12
8 22 2
1 2
2 2
)AX A
A
X XX
X XX
=
++
=
( )+( ) ( )
+ +
11.
(( )( ) +( )
=
( ) +( )+( ) ( )
=
X X
X XX X
X X
2 2
8 2 1 22 2
8 16 2XX X
XX X
or X
X
+( ) ( )=
+( ) ( )
+
2 27 18
2 27 18
412
6
2
12.AAB
ABAB AB
ABAB
A BB
=( )( ) +
( )( ) =
+
=(
12
6 22
122
82
32
813.))
( ) ( )( ) =
+ = + =
232
8 32A B
AB A
B AAB
XYZ
ZYXY
XYZ
ZX
XY
14.
XXZ X
Z ZX Z
X Y ZXZ
X X X
( )( ) +
( )( ) =
+
+ =( )(
2 2
2 2
3 223
23 2
15. )) ( )( ) +
( )( ) =
+ = +
X
X X X X
XY
32 3
2 23 2
26
36
46
2 3 46
2 2
16. +++
= +( )
+( )+
( )+( )( )
=
+ ++
31
11
31
31
2 2
YX
X XY X
Y YX Y
X X YY X(( )
+ ++
or X X YXY Y
2 23
Systematic Review 2CSystematic Review 2C1.
2.
XX
= =2 1 1 00 : correct
incoorrect: 2X+3X+6
=+
++
+ = +( )
= +
26
36
XX X
BX BcB
B X cB
X c3.11
27 549
9 3 69
3 61
3 6 3
2 2
22 2
= +
= ( )
=
=
X c
Y Y
Y Y Y
4.
= ( 22
8 4
2
2 4 2
2
4 21
4
2 4 3
3
3 2
3
22
)
5. X Y XY
Y
Y X Y X
Y
X Y X X
+ = +( )
=
+ = YY X X XY
AB
cB
AB
cB
A cB
X
+ = +
+ =( )( ) + =
+
2 2 2 1
222 2
22
4
( )
6.
7. ++ =( )( ) +
( )( ) =
+
+ =( )( ) +
Y X Y X Y
XX
X
77
4 74
7 47 4
28
55
5 55
8. XX XX
XX
XX
X X X X
( )( ) =
+ = +
= ( )( ) =
5
55
255
3 2 3 2 6
2 2 2
4 5 4 59. XX X
X X X X
4 5 9
2 2 2 2 0
24
2
6
1
10 10
+
+ ( )
( )
=
= = =
( )10.
11. 44 8
8
15 35
10
1
10
1100 000 000
2 2
( )
, ,
or
or
so
11
27 549
9 3 69
3 61
3 6 3
=
=
X c
Y Y
Y Y Y = ( 22
8 4
2
2 4 2
2
4 21
4
2 4 3
3
3 2
3
22
)
5. X Y XY
Y
Y X Y X
Y
X Y X X
+ = +( )
=
+ = YY X X XY
AB
cB
AB
cB
A cB
X
+ = +
+ =( )( ) + =
+
2 2 2 1
222 2
22
4
( )
6.
7. ++ =( )( ) +
( )( ) =
+
+ =( )( ) +
Y X Y X Y
XX
X
77
4 74
7 47 4
28
55
5 55
8. XX XX
XX
XX
X X X X
( )( ) =
+ = +
= ( )( ) =
5
55
255
3 2 3 2 6
2 2 2
4 5 4 59. XX X
X X X X
4 5 9
2 2 2 2 0
24
2
6
1
10 10
+
+ ( )
( )
=
= = =
( ) =10.
11. 44 8
8
15 35
10
1
10
1100 000 000
2 2
( ) =
= ( ), ,
or
or
so12. X
X Y Y
Y XX Y Y Y X
X Y
=
= =
+ +
33 2 1
3 53 2 1 3 5
3 5 2
13.
( )+
= = =
=
1 3 2 0 2 2
3 2 2
2 43 2 2 2
1X Y X X
A A B
B AA A B B A
( )
14.
+ ( )+ ( ) +
=
=
=
4
3 2 4 2 2 3 44
3
2 12
25
1 3
A B A B or B
A
P15.77
52
25
107
70 52
70 25
70 107
3502
1405
70
=
( ) = ( ) ( )
=
P
P
P 007
175 28 100
275 28
27528
9 2328
2 03
=
=
= =
+ =
P
P
P
X X16. . . .669
100 2 100 03 100 69
20 3 69
23
( )( ) + ( )( ) = ( )( )+ =
. . .X X
X X
XX
X
B B B B
B
=
= =
+ +( ) = + +( ) = + +
69
6923
3
7 2 3 7 4 3
7 28 2
217.
11 28 14
4
2 2 2
B or B
XYZ X Y Z X YZ XY Z XYZ
+
+ +( ) = + +
18.
19. 33 2 5 6 22
4 3 2 5 16 4 3 2 5 16
4 9 2
2
2 2
+ =
+ = + =
+ 55 16 36 2 5 16 55
6 3 4 8 3 13
9 4
2 2
2
= + =
+( ) ( ) + =
20.
(( ) + = + =
+ = + =
23 1
381 16 3 1
3
81 16 3 31
81 16 9 74
-
ALGEBRA 2
sYstEMAtic REViEW 2c - sYstEMAtic REViEW 2D
soLUtions 257
. . .669
100 2 100 03 100 69
20 3 69
23
( )( ) + ( )( ) = ( )( )+ =
. . .X X
X X
XX
X
B B B B
B
=
= =
+ +( ) = + +( ) = + +
69
6923
3
7 2 3 7 4 3
7 28 2
217.
11 28 14
4
2 2 2
B or B
XYZ X Y Z X YZ XY Z XYZ
+
+ +( ) = + +
18.
19. 33 2 5 6 22
4 3 2 5 16 4 3 2 5 16
4 9 2
2
2 2
+ =
+ = + =
+ 55 16 36 2 5 16 55
6 3 4 8 3 13
9 4
2 2
2
= + =
+( ) ( ) + =
20.
(( ) + = + =
+ = + =
23 1
381 16 3 1
3
81 16 3 31
81 16 9 74
Systematic Review 2DSystematic Review 2D1. incorrect: 1
3+ =
( )( )
12
1 23 2
++( )( ) =
+ =
= ( )
1 32 3
2 36
56
4 42 2 22.
3.
correct
X X XX
X X XX
==
=
+( ) ( )
= + = +
41
4
1 11
11
1
28 14
22
2
X X X X
X XX
X X
A
4.
5.77
7 4 27
4 21
4 2
81
102
2
22 2
= ( )
=
=
++
+
A
A A A
X X
= 2(2 )
6. == +( )
+( ) +( )+
+( )+( ) +( )
= + + +
8 21 2
10 12 1
8 16 10
XX X
XX X
X X 1101 2
18 261 2
18 26
3 22
X XX
X Xor X
X X
+( ) +( )=
++( ) +( )
+
+ +
77.
8.
74
92
74
9 22 2
7 184
114
Y Y Y Y
Y Y
AB
Bc
A c
= ( )( ) =
=
+ =(( )( ) +
( )( ) =
+
= =
B cB Bc B
Ac BBc
or
2
5 2 5 2 78 8 8 8 19. 88
12
1
2
2
1
81
8
7
3 3
3
3
310. ( ) = = = =
11.
12.
7 7 7 1
7
1 000 000 10 1
24
2 4 88
6
( ) = =
= =
( ) ( )
, ,
or
00 3
6
2
6
23
3 3 2 4
1 0
3 2 3 4
( ) =
=
+ ( ) + so X
A B A B
A B
A B13.(( )
+
( )=
= = =
2 1
6
23 3
3
1
3 1 1
11 1 1 1 1 1
2 1
A
A B
AA B A A B
A B or AB
A B A
B A A
A B
B A
3
3
18
3
18
3
2
2 4 2
1 1 3
2 2 4
1 1 314.
+
+= =
AA B
B A
B B
A
B
A
B
Aor B A
0 4
61 4
4 1
4
4 1
4
3
43
18 6
6 6
16
= =
=
+ ( )
=
( ) ( ) = ( )
=
4
12
25
37
70 12
70 25
70 37
702
1405
2
15. P
P
P 1107
35 28 30
28 5
528
528
=
=
=
=
P
P
P
16. 7 2 3 07
100 7 2 100 3 100 07
720
. .
. .
=
( )( ) ( )( ) = ( )( )X
X
=
=
= =
+ = ( )
300 7
420 7
4207
60
72 45 9 82 2
X
X
X
XY X Y XY Y17. ++( )
= ( ) ( )
( ) +
5
18 24 6 3 4
1 7 8 11
2 3 3
2
X
A AB A A B
n
18.
19. ==
( ) + = + =
= =
3
6 8 11 3
36 8 11 38 3 36 118 5
2n
nnn 00
508
254
6 14
6 6 100 1 14 5 9 4
12
2 2
n
B
B
=
= =
+( ) + = +(
20.
)) + = ++ = +
+ =
2100 1 14 5 9 4
144 99 14 45 4
144 99 14 491
B
B444 85 49
144 49 85144 36
36144
14
BBB
B
+ == =
= =
-
ALGEBRA 2
sYstEMAtic REViEW 2D - sYstEMAtic REViEW 2E
soLUtions258
( ) +
5
18 24 6 3 4
1 7 8 11
2 3 3
2
X
A AB A A B
n
18.
19. ==
( ) + = + =
= =
3
6 8 11 3
36 8 11 38 3 36 118 5
2n
nnn 00
508
254
6 14
6 6 100 1 14 5 9 4
12
2 2
n
B
B
=
= =
+( ) + = +(
20.
)) + = ++ = +
+ =
2100 1 14 5 9 4
144 99 14 45 4
144 99 14 491
B
B444 85 49
144 49 85144 36
36144
14
BBB
B
+ == =
= =
Systematic Review 2ESystematic Review 2E1.
2.
correct XX X X
: X+3X
= + =3 1 3
iincorrect: 2X+1
+ =
( )+( )( )
+ +( )
+( )=
3
21
3 11
2
XX
X XX
X XXX XX X
X
X XAX Y X
AX Y X A
+ ++( )
= +
+ + =
+ =
3 31
5 3
6 62
262
62
2
3.
XX Y X
B B
B
B B
B
B B
A
23 3
1 11
1
6
4 2
2
2 2
2
22
2
+
=( ) ( ) = = 4.
5. ++ =( ) +( )( )( ) =
+ +
612
6 16 2
12 2
12
AA
A AA
A or A
Systematic Review 2E1.
2.
correct XX X X
: X+3X
= + =3 1 3
iincorrect: 2X+1
+ =
( )+( )( )
+ +( )
+( )=
3
21
3 11
2
XX
X XX
X XXX XX X
X
X XAX Y X
AX Y X A
+ ++( )
= +
+ + =
+ =
3 31
5 3
6 62
262
62
2
3.
XX Y X
B B
B
B B
B
B B
A
23 3
1 11
1
6
4 2
2
2 2
2
22
2
+
=( ) ( ) = = 4.
5. ++ =( ) +( )( )( ) =
+ +
612
6 16 2
12 2
12
AA
A AA
A or A
6. 4 13
4 33
13
123X X
XX
XX
+ =( )( ) +
( )( ) =
+
7. XY
YX
X XY X
Y YX Y
X X Y
++
= +( )
+( )+
( )+( )( )
=
+ +
42
22
42
2 42 2
XX Yor X X Y
XY Y+( )( )+ +
+22 4
2
2 2
8. 31
2 31
2 11
3 2 21
Q QQ
Q QQ
Q Q
Q QQ Q
++ =
( )+( )
++( )+( )
=
+ ++( )
== ++( )
+
+
= + + (
5 21
5 2
2 2 2
2
2 3 3 1 2 3 3 1
QQ Q
or Q
Q Q
X X X9.))
=
= = =
( )( ) =
2 32
1
5 5
5 2 2
3
33 3 0
24
32
X or X
Y
YY Y10.
11.(( )( ) ( )
( )( )
=
( ) = ( ) = =
4 3 2424
3 23
2 3
5 1
5
49 7 7 7
or
12. 66
23
42
2 3 4 2
6 8 6 8
13. X X X X
X X X
( ) ( ) = == =
( )( ) ( )( )
+ ( ) XX orX
P P P P P P
P P P
( ) ( ) ( ) = =
22
42
3 1 4 2 3 1
8 3
1
14.
8. 31
2 31
2 11
3 2 21
Q QQ
Q QQ
Q Q
Q QQ Q
++ =
( )+( )
++( )+( )
=
+ ++( )
== ++( )
+
+
= + + (
5 21
5 2
2 2 2
2
2 3 3 1 2 3 3 1
QQ Q
or Q
Q Q
X X X9.))
=
= = =
( )( ) =
2 32
1
5 5
5 2 2
3
33 3 0
24
32
X or X
Y
YY Y10.
11.(( )( ) ( )
( )( )
=
( ) = ( ) = =
4 3 2424
3 23
2 3
5 1
5
49 7 7 7
or
12. 66
23
42
2 3 4 2
6 8 6 8
13. X X X X
X X X
( ) ( ) = == =
( )( ) ( )( )
+ ( ) XX orX
P P P P P P
P P P
( ) ( ) ( ) = =
22
42
3 1 4 2 3 1
8 3
1
14. + + ( )= =
+ =
( )( ) +
1 8 3 1 10
024 56
1 000 024 1
P P
F F
F
15. . .
, . ,, , .
,
,
000 1 000 56
24 1 000 560
1 024 560
( )( ) = ( )( )+ =
=
F
F F
F
FF
B
B
= =
+ =
+ =
(
5601 024
3564
10 23
3 16
178
323
196
158
24
,
16.
)) + ( ) = ( )
+ =
+ =
323
24 196
24 158
7683
4566
3608
256 76 45
B
B
B
2256 31
31256
100 2 3 07 230 7
1
B
B
X Y X Y
=
=
( ) = 17.18.
. .
,0000 009 02 3
9 20 3 000 9 3 020
6 9
. .
, ,
A
A A
+ +( ) =+ + = +
( ) 19. 22 9 8 4 723
2 9 8 3
43
9 8 24
43
= +( )
= +( )
= +
Y Y
Y Y
Y Y
= +
=
=
=
24 8 9
43
723
17
683
17
117
683
17 117
68
Y Y
Y
Y
Y
55143
1 13
11 4 7 3 9 14 2
7
2
2
= =
( ) = ( )
( )
Y or
R R20.
77 6 1449 7 6 14
7 6 141 14
114
11
= ( ) = =
=
= =
R
RRR
R
44
-
ALGEBRA 2
sYstEMAtic REViEW 2E - LEsson PRActicE 3B
soLUtions 259
= +
=
=
=
24 8 9
43
723
17
683
17
117
683
17 117
68
Y Y
Y
Y
Y
55143
1 13
11 4 7 3 9 14 2
7
2
2
= =
( ) = ( )
( )
Y or
R R20.
77 6 1449 7 6 14
7 6 141 14
114
11
= ( ) = =
=
= =
R
RRR
R
44
Lesson Practice 3ALesson Practice 3A1.
2.
85 000 000 8 5 10
341 3
7, , .
. .
=
= 441 10
00038 3 8 10
9 700 000 000 9 7 10
1
4
=
=
3.
4.
. .
, , , . 99
5 3
000073 0054
7 3 10 5 4 10
7 3 5 4
5. . .
. .
. .
=
( ) ( ) =(
)) ( ) = =
10 10
39 42 10 3 942 10
58 000 000
5 3
8 7. .
, ,6. (( )( ) =( ) ( ) =( ) ( ) =
650
5 8 10 6 5 10
5 8 6 5 10 10
7 2
7 2
. .
. .
337 7 10 3 77 10
098 006
9 8 10 6 0
9 10
2
. .
. .
. .
=
( )( ) =( )
7.
( ) =( ) ( ) = =
10
9 8 6 0 10 10
58 8 10 5 88 10
3
2 3
5
. .
. .
=
( ) ( )
4
9 6
1 800 000 000 2 400 000
1 8 10 2 4 10
8. , , , , ,
. . ==
( ) ( ) = =
1 8 2 4 10 10 4 32 10
27 000 009
2 7
9 6 15. . .
, .
.
9.
( ) ( ) =( )( ) =
=
10 9 0 10
2 7 9 0 10 10
3 10 3
4 3
4 3
7
.
. .
.
=
( ) ( ) =
10
0021 340 000
2 1 10 3 4 10
2 1
6
3 5
10. . ,
. .
.
33 4 10 10
62 10 6 2 10
00042000
3 5
8 9
.
. .
.
.
( )( ) =
11.006
4 2 10 6 0 10
4 2 6 0 10 10
4 5
4 5
= ( ) ( ) =( )( ) =
. .
. .
.. .
, , ,,
.
7 10 7 0 10 7 1 7
6 800 000 000430 000
6
1 0 = = =
=12.
88 10 4 3 10
6 8 4 3 10 10 1 58 10
9 5
9 5 4
( ) ( ) =( )( )
.
. . .
133. 2 8 7
2 8 7 1
3
3 2
3 3 0
4 2
2
3
1
3
X
X Y
XYXY
X Y
X Y
Y
Y
Y
X
X
+ =
+
( )( ) = =
10 9 0 10
2 7 9 0 10 10
3 10 3
4 3
4 3
7
.
. .
.
=
( ) ( ) =
10
0021 340 000
2 1 10 3 4 10
2 1
6
3 5
10. . ,
. .
.
33 4 10 10
62 10 6 2 10
00042000
3 5
8 9
.
. .
.
.
( )( ) =
11.006
4 2 10 6 0 10
4 2 6 0 10 10
4 5
4 5
= ( ) ( ) =( )( ) =
. .
. .
.. .
, , ,,
.
7 10 7 0 10 7 1 7
6 800 000 000430 000
6
1 0 = = =
=12.
88 10 4 3 10
6 8 4 3 10 10 1 58 10
9 5
9 5 4
( ) ( ) =( )( )
.
. . .
133. 2 8 7
2 8 7 1
3
3 2
3 3 0
4 2
2
3
1
3
X
X Y
XYXY
X Y
X Y
Y
Y
Y
X
X
+ =
+( )
44 2
2 3 1 3 4 2
2 3 1 3 4
2 8 7
2 8 7
Y
Y Y Y X X Y
Y Y X
=
+ =
+
+ ( ) + ( )YY
Y Y X Y Y X Y
AX
X
BX
B
=
+ = +
2
2 2 1 2 2 1 2
3
3
3
2 8 7 6 7
14.
+ +
+ =
+ =
1 2 2
3 3 1 3 1 1 1 2 2
3 3 1 1
ABX
X B
AX X B X B AB X X B
AX B XX AB X
AX B X AB X
AB
3 1 2 1 2
6 2 3 1 1
13 13
+ =
+
+
+ ( ) + ( )
15. AAB
A B A B
AB A B A B A B
AB
+ =
+ + =
+
2 1 1
1 1 1 2 1 1 1
1
3
3 13 3
3 133 3
6 13 6 13
3
1 2 1 1 1
1 3 0 1 3
A B AB
AB A B AB A
+ + ( )
+ =
+ = +
16. XX Y X Y X Y X Y
X Y X Y
2 2 3 0 1 3 1 1
2 3 2 0 1 1
2 6
3 2 6
+ ( ) + ++ =
+ ( )( ) +
=
+
3 1
1 2 2 23 12X Y X Y
Lesson Practice 3BLesson Practice 3B1.
2.
360 000 000 3 6 10
00000
8, , .
.
=
001 1 10
0059 5 9 10
425 000 4 25 10
7
3
5
=
=
=
3.
4.
5.
. .
, .
.00063 1 200 000
6 3 10 1 2 10
6 3 1 2 10
3 6
=
( ) ( ) =( )
, ,
. .
. . ( ) = ( )( ) =
( )
3 6 3
4
10 7 56 10
16 000 007
1 6 10 7 1
.
, .
.
6.
00
1 6 7 10 10
11 2 10 1 12 10
92
3
4 3
1 2
( ) =( ) ( ) = =
.
. .
.7. (( )( ) =( ) ( ) =( ) (
.
.
.
0009
9 2 10 9 10
9 2 9 10 10
1 4
1 4)) = =
82 8 10 8 28 10
2 300 000 4 000 000 000
5 4. .
, , , , ,
-
ALGEBRA 2
LEsson PRActicE 3B - sYstEMAtic REViEW 3c
soLUtions260
1.
2.
360 000 000 3 6 10
00000
, , .
. 001 1 10
0059 5 9 10
425 000 4 25 10
7
3
5
=
=
=
3.
4.
5.
. .
, .
.00063 1 200 000
6 3 10 1 2 10
6 3 1 2 10
3 6
=
( ) ( ) =( )
, ,
. .
. . ( ) = ( )( ) =
( )
3 6 3
4
10 7 56 10
16 000 007
1 6 10 7 1
.
, .
.
6.
00
1 6 7 10 10
11 2 10 1 12 10
92
3
4 3
1 2
( ) =( ) ( ) = =
.
. .
.7. (( )( ) =( ) ( ) =( ) (
.
.
.
0009
9 2 10 9 10
9 2 9 10 10
1 4
1 4)) = =
82 8 10 8 28 10
2 300 000 4 000 000 000
5 4. .
, , , , ,8. ,,
. .
. .
000
2 3 10 4 0 10
2 3 4 0 10 10 9
6 12
6 12
=
( ) ( ) =( ) ( ) = ..
. .
.
.
2 10
0024 000003
2 4 10 3 10
2 4
18
3 6
=
( ) ( ) = 9.
3 10 10
8 10 8 10
29 000 000 15 0
3 6
3 2
( )( ) = =
.
, , ,10. 000
2 9 10 1 5 10
2 9 1 5 10 10 1 93
7 4
7 4
=
( ) ( ) =( )( )
. .
. . .
103
11. 9 600 000 000 00002
9 6 10 2 10
9 6
12 2
, , , ,.
.
.
=
( ) ( ) = 2 10 10 4 8 10
00016000008
1 6 1
12 2 14( )( ) = =
.
..
.12. 00 8 10
1 6 8 0 10 10
2 10 2 1
4 6
4 6
2
( ) ( ) =( )( ) =
=
. .
. 001
12 3 6
1 3
3 2 0
1
12 3 6 1 3 3
13. R R R
R s
R R R
R
R R R R s R R
+ =
+
+ ( )+ + ( ) + ( )+ + ( )=
+ =
2 0 1
12 3 6 1 3 3 2 0 1
14 3
R R
R s R
R s ++ = +R R s0 14 3 1
14. 2 8 3
2 8
3 3
1 1
5 5 1 4 5
2 2
3 3 1 1
X Y
X Y
X YXY
X Y
X Y
X Y X Y X
+ =
+ 55 5 1 14 5 2 2
1
3 1 3 1 5 1 5 1
3
2 8
Y X Y X Y X Y
X Y X Y
+ + + ( ) +
=
+(( ) + ( ) + ( )
=
+ =
X Y
X Y X Y X Y X Y X
4 2 5 2
4 4 4 42 3
4 42
3
2 83
10 YY
A B B
B BA
B B B B A
3
0 44
2 5
4 4 2 5
3
16 4 4
16 1 4 4
1
15. + =
( ) + =
66 4 4
16 4 4 16 4 4
4 4 2 5
4 3 43
B B A
B B A BB
A
+ =
+ = +
+ ( )+ ( )
166. 2
2
6 3 3 2 1 0 2 4 3
6 2 3 3 1 0 2
A B c A c c c A B
A B c c
+ ( ) + ++ =
+ AA B
A B c A B c
A c
B
A c
B
A c
B
4 3
4 3 3 4 3 3
4 3
3
4 3
3
4 3
3
=
+ =
+ =
14. 2 8 3
2 8
3 3
1 1
5 5 1 4 5
2 2
3 3 1 1
X Y
X Y
X YXY
X Y
X Y
X Y X Y X
+ =
+ 55 5 1 14 5 2 2
1
3 1 3 1 5 1 5 1
3
2 8
Y X Y X Y X Y
X Y X Y
+ + + ( ) +
=
+(( ) + ( ) + ( )
=
+ =
X Y
X Y X Y X Y X Y X
4 2 5 2
4 4 4 42 3
4 42
3
2 83
10 YY
A B B
B BA
B B B B A
3
0 44
2 5
4 4 2 5
3
16 4 4
16 1 4 4
1
15. + =
( ) + =
66 4 4
16 4 4 16 4 4
4 4 2 5
4 3 43
B B A
B B A BB
A
+ =
+ = +
+ ( )+ ( )
166. 2
2
6 3 3 2 1 0 2 4 3
6 2 3 3 1 0 2
A B c A c c c A B
A B c c
+ ( ) + ++ =
+ AA B
A B c A B c
A c
B
A c
B
A c
B
4 3
4 3 3 4 3 3
4 3
3
4 3
3
4 3
3
2
2 3
=
+ =
+ =
Systematic Review 3CSystematic Review 3C1.
2.
62 000 6 2 10
75 7 5 1
4, .
. .
=
= 00
0048 4 8 10
3 080 000 3 08 10
62 00
1
3
6
=
=
3.
4.
5.
. .
, , .
, 00 75
6 2 10 7 5 10
6 2 7 5 10 10
4 1
4 1
( )( ) =( ) ( ) =( )
.
. .
. . (( ) = =
( )( ) =
46 5 10 4 65 10
3 080 000 0048
3 08
3 4. .
, , .
.
6.
110 4 8 10
3 08 4 8 10 10
14 784 10
6 3
6 3
( ) ( ) =( ) ( ) =
.
. .
. 33 4
6
1 4784 10
3 080 000 75
3 08 10 7 5
=
( ) ( ) =( )
.
, , .
. .
7.
( ) =( )( ) =
10
3 08 7 5 10 10
4107 10 4 107 1
1
6 1
7
. .
. .
00
62 000 0048
6 2 10 4 8 10
6 2
6
4 3
8. , .
. .
.
( ) ( ) =( ) ( ) =
44 8 10 10 1 29 104 3 7. .( )( ) 9. 8 2
8 2
8 2
21
2 2 2 1
2 2 2
XXY YX Y XY
X
X Y X Y XYX
X Y X Y X
+ =
+ =
+
22 2 2 2
2 12
3
3
22
2
10
4 12 8
4
Y X Y X Y
X X X
X
XX
X
X
=
+ +( )
=
+
10.
11 2 34
2 2
1 2 34
4
5
12 8
4 12 8
4 12
( )( )( )
+
+ + =
+ + =
+
X X X
X
X X X
X
X X ++ = + +
+ +
+ + =
81
4 12 8
12 4 8
4 9 8
4
5
5
2 1
1
X X
X X
A AB B
BAB
A
or
-
ALGEBRA 2
sYstEMAtic REViEW 3c - sYstEMAtic REViEW 3D
soLUtions 261
9. 8 2
8 2
8 2
21
2 2 2 1
2 2 2
XXY YX Y XY
X
X Y X Y XYX
X Y X Y X
+ =
+ =
+
22 2 2 2
2 12
3
3
22
2
10
4 12 8
4
Y X Y X Y
X X X
X
XX
X
X
=
+ +( )
=
+
10.
11 2 34
2 2
1 2 34
4
5
12 8
4 12 8
4 12
( )( )( )
+
+ + =
+ + =
+
X X X
X
X X X
X
X X ++ = + +
+ +
+ + =
81
4 12 8
12 4 8
4 9 8
4
5
5
2 1
1
X X
X X
A AB B
BAB
A
or
11.
++ + =
+ + =
+ +
+ ( )+ ( )9 8
4 9 8
4 9 8
2 1 1
2 1 1
AB B B AB
A AB AB
A A ABB A AB
A BA AB B
A B AB B
A
= +
+ =
+ =
+ ( )
13 8
2 3 5
2 3 5
2
1 1
1 1
12.
00 3 5 2 1 3 5
2 3 5 3 3
B AB B B AB B
B AB B AB B
+ = ( ) + =+ = or 3B(AA 1)
=( ) ( ) =
13. 75 505
5 15 105
15 10
2A Y AXAX
A AY XAX
AY XXX
AY XX
XY YY
Y XY
X
or 5 3 2
12 303
3 4 103
4
( )
+ =( ) +( ) =14.
++ = +
++ =
( )+( )
101
4 10
13
221 2
X
YX Y
Y YX
or 2(2X + 5)
15.YY
XY X
Y Y XY X
Y X
( ) ++( )+( )
=
( ) + +( )+( )
= + +
3 12 1
2 3 12 1
2 3 32
22 2
37
37
77
3 77
103
XY Y
AB
BB
AB
B AB
+
+ =( )( ) +
( )( ) =
+16.
17. (( ) = ==
( )( )
+
43 4 12
3 2 4
2 1 1
3 2 4
10 10
18. X X Y
Y Y X
X Y
Y 22 1 1
1 4
3 1
1 4 3 1 1 1 4 3 0 7
+ ( )
+ +
= =
= =
X
X Y
Y X
X Y Y X X Y X Y ==
( ) =
+ =
Y
XY X Y X Y XY
YX
XY
YY
Y XX
7
2 2
2 3 2
2 3
3 4 3 419.
20. ( )YY
YXY
Y Y X X Y YX
YX YX
+ = + = + 4
2 1 3 14 1
23
Systematic Review 3DSystematic Review 3D1.
2.
25 000 000 2 5 10
0000
7, , .
.
=
339 3 9 10
000000014 1 4 10
760 7 6 10
5
8
2
=
=
=
.
. .
.
3.
4.
5.. . .
. .
.
000000014 000039
1 4 10 3 9 10
1
8 5
( )( ) =( ) ( ) =
44 3 9 10 10 5 46 10
25 000 000 760
8 5 13( ) ( ) = ( )
. .
, ,6. (( ) =
( ) ( ) =( ) ( ) =
2 5 10 7 6 10
2 5 7 6 10 10
19 10
7 2
7 2
. .
. .99 10
8
1 9 10
000000014 000039
1 4 10
=
( ) ( ) =( )
.
. .
.
7.
33 9 10
1 4 3 9 10 10
359 10 3 59
5
8 5
3
.
. .
. .
( ) =( )( ) =
=
( ) ( ) =( ) ( ) =
10
25 000 000 760
2 5 10 7 6 10
4
7 2
8. , ,
. .
22 5 7 6 10 10
329 10 3 29 10
7 2
5 4
3 2 1
. .
. .
( )( ) = =
9. X Y XY
=
+ ( ) + ( )
4 3
4 3
2 2 2 2
2 1
3 1 2 2 2 2 2
Y X YY
X Y
X X
X YY
Y XY
X YY
X
X Y
Y
Y X
Y
X Y
X
X Y Y X Y
2 1
2 2
1
0 2
1
2
3
2 2 1 2 1
4 3
4 1
+
=
=
( ) 334 3
4
2 3
2 2 1 2 1 2 3
2 2 1
X YX
X Y X Y X Y
X Y X Y
+ ( ) + ( )
=
=
33 4 3
30 11
1 22
2 1
1 3
1 1
3
X Y or X Y XY
YX
X Y
Y X
X Y
Y X
10.22
0 0 1
4 2 2
2 1
1 3
1 1
3 2
18
30 11 1 1
=
( )
X X
Y X Y
X Y
Y X
X Y
Y X(( ) =
=
X Y X Y
X Y
Y X
X Y
Y XX Y
1 4 2 2
2 1
1 3
1 1
3 23 230 11
300 11
30 11
2 1 1 3 1 1 3 2 3 2
1 2
X Y Y X X Y Y X X Y
X Y X
=
1 4 3 2
2 4 3 230 11 1
Y X Y
XY XY X Y
or
-
ALGEBRA 2
sYstEMAtic REViEW 3D - sYstEMAtic REViEW 3E
soLUtions262
11. 13 2 4
24
131
2 4
24
0
3 1
1
2 2
2
3
2
0
A
B
A B
B AA
B B
B
A A
A
B
B
=
22
3 22
2 2
13 2 4 1
4 6
13 2 1
611 1
6
=
( )
( ) =
=
A A AB
A AB
AB
12.. 3 17 42
3 17
1 3 2 1 2 2
1 3 2 1 2
ABB B BA A B A
AB A
+ + ( ) + =
BB AB
AB AB AB or
AB AB A
B
=
42
3 17 42
3 17 42
2
2 2
22
13.. 48 72
24
24 2 3
242 3
12 3
2 2
2
2
2B Y B Y
B
B Y Y
BY Y Y Y
+ = +( )
=
+ = + = 55
21 3514
7 3 57 2
3 52
2
2
Y
X XYX
X X YX
X Y
XY
14.
15.
= ( )
( ) =
+117
22 2
1 27 1
2 1
2
+
=
( )+( ) ( )
+ +( )
( ) +( )=
XX X
Y XY
X Y
X X 22 7 11 2
2 4 7 71 2
2
2( ) + +( )+( ) ( )
= + ++( ) ( )
YY X
X X YY X
or
XX X YXY X Y
A
A
A A
A A
2
2
2
2 2
4 7 72 2
77
7
7 7
+ ++
+ =( )( ) +
( )16.
77
49
7
2 2 2
1
2
3
2
32
3 2 6
6
( )= +
( ) = ( ) = ( ) =
( )( )
A
A
17.
==
= =
+ ( )+
+ ( )
164
6 3 2 7
2 1
6 2 7 3
2 118. A B A A
B B
A B
B
AA B
B
A B B A B A B or BA
A B
+
=
= =
1 3
3
1 3 3 1 3 3 1 66
2 5219. 33 5
2 3 2 5
6
1 1 3
2 5 1 1 2 5 3
2 1
A B B
A B A B A B B
A
( ) =( ) ( ) =
+ BB A B
A B A B or BA
B
A
5 1 2 5 3
1 6 2 26 2
10
6 10 6 10
+ + ( )
=
22
2
2
3
3
2 2 3
1 3 1 2
20. X
Y
X YX
Y
X
X Y
XY
XY
Y X
X X Y Y X
+ = + =
+
( )11 1 2 3 2 3 2 3
2 33
2
Y Y X X Y X Y or
X Y Y
X
= +
+
A B A A
B B
A B
B
AA B
B
A B B A B A B or BA
A B
+
=
= =
1 3
3
1 3 3 1 3 3 1 66
2 5219. 33 5
2 3 2 5
6
1 1 3
2 5 1 1 2 5 3
2 1
A B B
A B A B A B B
A
( ) =( ) ( ) =
+ BB A B
A B A B or BA
B
A
5 1 2 5 3
1 6 2 26 2
10
6 10 6 10
+ + ( )
=
22
2
2
3
3
2 2 3
1 3 1 2
20. X
Y
X YX
Y
X
X Y
XY
XY
Y X
X X Y Y X
+ = + =
+
( )11 1 2 3 2 3 2 3
2 33
2
Y Y X X Y X Y or
X Y Y
X
= +
+
Systematic Review 3ESystematic Review 3E1.
2.
9 400 9 4 10
00000053
3, .
.
=
= 55 3 10
012 1 2 10
160 000 1 6 10
9 40
7
2
5
.
. .
, .
,
=
=
3.
4.
5. 00 012
9 4 10 1 2 10
9 4 1 2 10 10
3 2
3
( )( ) =( ) ( ) =( )
.
. .
. . 22
1 211 28 10 1 128 10
160 000 00000053
( ) = =
( )( ) =. .
, .6.
11 6 10 5 3 10
1 6 5 3 10 10
8 48 1
5 7
5 7
. .
. .
.
( ) ( ) =( ) ( ) =
00
9 400 012
9 4 10 1 2 10
9 4 1
2
3 2
( ) ( ) =( ) ( ) =
7. , .
. .
.
.. .
, .
2 10 10 7 83 10
160 000 00000053
3 2 5( )( ) ( ) ( )
8. ==
( ) ( ) =( )( ) =
1 6 10 5 3 10
1 6 5 3 10 10
302
5 7
5 7
. .
. .
.
( )
( )
10 3 02 10
25 11 2
12 11
1 2 0 0
1
.
9. X YYX
Y X
XXY
X
X YY
X Y Y XX Y Y
X Y
=
( )( )
=
2
1 2 1 12 1 2
2
25 111 1 2
25 11XX Y Y
X Y Y or Y
XY
=
2 1 2
2 22
2
2
14 2 14 2
-
ALGEBRA 2
sYstEMAtic REViEW 3E - LEsson PRActicE 4A
soLUtions 263
10. 13 7 5
13 7
2
2
2
1 1
0 1
3
2 1 2
X Y
XY
X Y
Y X
X Y X
Y
X YX Y X
+ =
22 1 1 1 1 3
1 3 2 4
5 1
13 7 5
13
Y X Y Y XY
XY X Y XY or
XY
+ ( ) = +
+
=
7 5
3 22 4
3 4
3 24
2 1
22
2 1 2
X Y X
Y
AB
BB
A AA B
A B B A
11.
22 1 2
2 1 2 2
22
2
4
3 4 4
3 4 4
A A B
A B AB A B
or AB
AB B
A
=
112. 4 3 5
4 3 5
1 1 2 3 3 1 1 1
2
A BA B AB B B A B A
B AB B
+ =
+ 22 23= AB B
13. 6 412
2 3 22 6
3 26
36
2
2 3 2
2
X XX
X X XX
X X X
+ =( ) +( )
( )( ) =
+ = + XX X X
X XX
X XX
X
2 2
2 2
6 2 3
32 4 168
4 8 44 2
8
= +
+ + =( ) + +( )
( ) =14.
22 242
82 2
42
41
12
2 4 12
2
4
+ + = + + =
+ + = + +
XX
XX
XX X
XX
XX
AA
15.++
+ =( )
+( )( )+ +
( )+( )
=
+ ++
56 4
56 5
5
4 6 305
2
AA A
A AA
A A
A AA A(( )
+ +
+
+ = + = +
or A A
A AX
X Y
YXY XY
YXY
Y
4 6 30
52 1 2 1 2
2
2
216.
XXY
17. ( ) = = = = ( )( ) =
( ) ( ) 4 4 4
1
4
14 4
116
21
2 1 2
2
118. 3
33 3
3
3 3 1 2
1 2 4 33 1 3 4 1 3 2 2A B c
c A BA A BB c c
= =
44 1 2 4 2 42 4
2 2 3 4
81 81
5
A B c AB c or A
B c
A B A AB
=
+19. 22
2 2 3 4 2 2 3 1 2
2 3 3 1
5 5
25 25
( ) =+ =
+
A B A A B A B
A B A B or 25 252 3
3
3
1
3
3
3
1 1
1 3
A B
AB
XY
X
Y
Y X
X
XX
Y Y
X Y X
+
+ = +
20. ( ) 111 34
1 3 1 1 3
4 1 2 42
1
Y X
X X Y X Y X
X X Y or X YX
=
+ =
+ +
3
33 3
3
A B c
c A BA A BB c c
44 1 2 4 2 42 4
2 2 3 4
81 81
5
A B c AB c or A
B c
A B A AB
=
+19. 22
2 2 3 4 2 2 3 1 2
2 3 3 1
5 5
25 25
( ) =+ =
+
A B A A B A B
A B A B or 25 252 3
3
3
1
3
3
3
1 1
1 3
A B
AB
XY
X
Y
Y X
X
XX
Y Y
X Y X
+
+ = +
20. ( ) 111 34
1 3 1 1 3
4 1 2 42
1
Y X
X X Y X Y X
X X Y or X YX
=
+ =
+ +
Lesson Practice 4ALesson Practice 4A1.
2.
3 2 6 2 3 6 2 9 2
5 7 2 5 5 7 2
+ = +( ) = = 55
6 8 6 8 2
4 3 1
cannot be simplified
3.
4.
X X X X = ( ) = + 66 3 4 16 3 20 3
2 5 3 6 2 3 5 6 6 30
10 5
2 5
1
= +( ) =( )( ) = ( )( ) =
=
5.
6. 002
5
9 2
9 2 18
=
( )( ) =( )( ) =
7. X Y
X Y XY
8. 16 20
8 10
16 28
2 21
2 2= = =
9.
10.
11.
12.
5
2
5 2
2 2
5 2
4
5 22
4 6
3
4 21
4 2
12
6
21
2
9 27
= = =
= =
= =
22
9 27 2
2 2
9 54
4
9 9 62
9 3 62
27 62
2
5
4
6
2 5
5 5
4 6
= = =
=( )
=
+ = +13.66 6
2 5
25
4 6
36
2 55
4 66
2 55
2 63
2 5 35 3
2 6 53 5
=
+ = + =
+ =( )
( ) +( )
(( ) =
+ = +
+( ) =
6 515
10 615
6 5 10 615
2 3 12 2 18
3 12 2 2 18
14.
22
3 24 2 36 3 4 6 2 6
3 2 6 12 6 6 12
2 7
=
= ( ) = ( ) =
+ =15. X X XX X
X X X X
X X
2
2 2
7
7 7
2
4
7
49
22
77
2 72 7
7 27 2
+ =
+ = + =
( )( ) +
( )( ) ==
+
7 2 2 714
4 2 10 20 4 2 10 4 20
8 10 4 4 5 8 10
X X
-
ALGEBRA 2
LEsson PRActicE 4A - sYstEMAtic REViEW 4c
soLUtions264
22
9 27 2
2 2
9 54
4
9 9 62
9 3 62
27 62
2
5
4
6
2 5
5 5
4 6
=
+ = +13.66 6
2 5
25
4 6
36
2 55
4 66
2 55
2 63
2 5 35 3
2 6 53 5
=
+ = + =
+ =( )
( ) +( )
(( ) =
+ = +
+( ) =
6 515
10 615
6 5 10 615
2 3 12 2 18
3 12 2 2 18
14.
22
3 24 2 36 3 4 6 2 6
3 2 6 12 6 6 12
2 7
=
= ( ) = ( ) =
+ =15. X X XX X
X X X X
X X
2
2 2
7
7 7
2
4
7
49
22
77
2 72 7
7 27 2
+ =
+ = + =
( )( ) +
( )( ) ==
+
( ) = ( ) = =
7 2 2 714
4 2 10 20 4 2 10 4 20
8 10 4 4 5 8 10
X X
16.
44 2 5
8 10 8 5
( ) =
Lesson Practice 4BLesson Practice 4B1.
2.
7 5 7 5 2
2 10 4 10
2
A A A A = ( ) =+ =
+ 44 10 6 10
6 3 6 5 6 3 6 5
3
( ) =+ = +3.
4.
cannot be simplified
111 5 11 3 5 11 2 11
3 6 3 5 3 3 6 5 9 30
24
= ( ) = ( )( ) = ( )( ) =5.
6. 114
6 2
4 14
2
4 71
4 7
7 2 7 2
14 142
= = =
( )( ) = ( )( ) ==
7.
8.
A A A A
A A
114
7
147
2
3 7
2
3 7 2
2 2
3 14
4
2
X
X
X
Y
X Y
Y Y
X Y
Y
X YY
= =
= = =
= =
9.
10. ==
= = = =
= =
= =
3 142
2 3
6
2
2
2 2
2 2
2 2
4
2 22
21
2
5 5
10
5
2
5 2
2
11.
12.22
5 2
4
5 22
= =
13. 6
2
10
7
6 2
2 2
10 7
7 7
6 2
4
10 7
49
6 22
10 77
3 21
10 7
+ = + =
+ = + =
+77
3 2 71 7
10 77
21 2 10 77
6 2 7 8 5
2 7 6 8 5 6 2
=( )
( ) + =
+
+( ) =+ =
14.
442 8 30+
+ = + =
+ = ( )
15. B
A
A
B
B A
A A
A B
B B
B AA
A BB
B A BA BB
A B AB A
B A A BAB
B A A BAB
( ) + ( )
( ) =
+2 2 2 2
11 3 2
or
16. 44 2 60
33 24 22 60 33 4 6 22 4 15
33 2 6 22 2 15 66
+( ) =+ = + =
( ) + ( ) = 66 44 15+
Systematic Review 4CSystematic Review 4C1. 3 169 3 169 3 13 394 4 2A A A A= = ( ) = 22
3 4 3 4 7
3 2 4 8 3 4 2 8
12 16 12 4
2.
3.
X X X X+ = +( ) =( )( ) = ( )( ) =
= (( ) =+( ) = + =
+ = ( ) + ( ) = +
48
2 6 2 5 8 6 2 2 5 8 2
6 4 5 16 6 2 5 4 12 20
4.
==
= =
= =
= = ( ) =
32
5 30
6
5 51
5 5
56
8
71
7
2 27 2 9 3 2 3 3 6 3
5.
6.
7.
8. 44 75 4 25 3 4 5 3 20 3
5
3
5 3
3 3
5 3
9
5 33
= = ( ) =
= = =9.
-
ALGEBRA 2
sYstEMAtic REViEW 4c - sYstEMAtic REViEW 4D
soLUtions 265
10. 3
5
4
6
3 5
5 5
4 6
6 6
3 5
25
4 6
36
3 55
4 66
3 55
2 63
3 5
+ = + =
+ = + =
+ = 335 3
2 6 53 5
9 5 10 615
6 100 000045
( )( ) +
( )( ) =
+
( )( ) =11. , .66 1 10 4 5 10
6 1 4 5 10 10
27 45
3 5
3 5
. .
. .
.
( ) ( ) =( ) ( ) =
110 2 745 10
0000098 140
9 8 10 1
2 1
6
=
( )( ) =( )
.
.
. .
12.
44 10
9 8 1 4 10 10
13 72 10 1 372 1
2
6 2
4
( ) =( ) ( ) = =
. .
. . 00 3
13. 630 000 9 000 000 000
6 3 10 9 105 9
, , , ,
.
( ) ( ) =( ) ( ) =
66 3 9 10 10
7 10 7 10
000093 00
5 9
4 5
.
.
. .
( )( ) = =
( )
14. 0000006300
9 3 10 6 10
3 10
9 3 6 1
5 8
2
( )( ) =
( ) ( )
=
( )
.
. 00 10
3 10
55 8 10
3 10
55 8 3 10
5 8
2
13
2
13
( )
=
=
( )
.
. 110
18 6 10 1 86 10
2
15 14
( ) = = . .
15. 3 6 4
3
2 4 2
2
3
1 1
4
3 2
2
A B c
AB
ABc
c B
AB c
c B
A B
+ =
44 2 1 23
1 1
4
3 2
3 2 2
6 4
3 6
c A B ABc
c B
AB c
c B
A B c A
+ =
+ BBc cB AB c
c B
A B c AB c AB c c
=
+
3 1 14 1
3 2
3 2 2 2 2 4 1
4
3 6 4
=
+ =
+
3 2
3 2 2 2 2 2 2
3 2 2
3 6 4
3 2
B
A B c AB c AB c
A B c ABB c orA B c
AB
c
2 23 2 2
2
23 2 +
16. 25
310
25
10 25
10 310
10 25
205
3010
X X
X X
X X
=
( ) ( ) = ( )
==
==
( )( ) =( )( )
250
4 3 250250
2 3
2 3
2 5
2 1
X XX
X Y XY
X Y
17.
XX Y X Y
X Y Z X Y Z
X Y
1 5 3 6
5 2 2 0 4 3
5 0 2
6
36 9
36 9
=
=
( )
18.
44 2 3
5 25
24 4
53
30
3 53
3
Z
X Y Z or X Z
Y
X
X
( )
( ) =
=
( ) =
19.
(( )
=
=
= =
+ = +( )
30
153
90
5 90905
18
3 20 10 5
10 3
X
X
X
X X20. . .
. XX X
X X
( ) + ( )( ) = ( )( ) + ( )( )+ = +
10 20 10 10 10 5
3 200 100 520
.
00 100 5 3100 2100
250
= =
= =
X XX
X
16. 25
310
25
10 25
10 310
10 25
205
3010
X X
X X
X X
=
( ) ( ) = ( )
==
==
( )( ) =( )( )
250
4 3 250250
2 3
2 3
2 5
2 1
X XX
X Y XY
X Y
17.
XX Y X Y
X Y Z X Y Z
X Y
1 5 3 6
5 2 2 0 4 3
5 0 2
6
36 9
36 9
=
=
( )
18.
44 2 3
5 25
24 4
53
30
3 53
3
Z
X Y Z or X Z
Y
X
X
( )
( ) =
=
( ) =
19.
(( )
=
=
= =
+ = +( )
30
153
90
5 90905
18
3 20 10 5
10 3
X
X
X
X X20. . .
. XX X
X X
( ) + ( )( ) = ( )( ) + ( )( )+ = +
10 20 10 10 10 5
3 200 100 520
.
00 100 5 3100 2100
250
= =
= =
X XX
X
Systematic Review 4DSystematic Review 4D1. 4 25
644 25
64
4 58
20
2 2X X
X
= =
=( ) 88 522 10 3 5 2 10 3 5
8 11
X X=
= 2.
3.
can't be simplified
(( )( ) = ( )( ) == ( ) =( )
2 11 8 2 11 11
16 121 16 11 176
3 8 10 9 54. ==
=
= =
= =
8 10 3 9 5 3 8 30 9 15
4 48
8
4 61
4 6
84
2
421
42
5 8
5.
6.
7. 00 5 16 5 5 4 5 20 5
6 125 6 25 5 6 5 5 30 5
= = ( ) == = ( ) =8.
-
ALGEBRA 2
sYstEMAtic REViEW 4D - sYstEMAtic REViEW 4D
soLUtions266
8852
2 10 3 5 2 10 3 5
8 11
X X=
= 2.
3.
can't be simplified
(( )( ) = ( )( ) == ( ) =( )
2 11 8 2 11 11
16 121 16 11 176
3 8 10 9 54. ==
=
= =
= =
8 10 3 9 5 3 8 30 9 15
4 48
8
4 61
4 6
84
2
421
42
5 8
5.
6.
7. 00 5 16 5 5 4 5 20 5
6 125 6 25 5 6 5 5 30 5
= = ( ) == = ( ) =8.
9.
10.
7
2
7 2
2 2
7 2
4
7 22
9
3
6
2
9 3
3 3
6 2
2 2
9 3
9
6 2
4
9 33
= = =
+ = + =
+ = ++ =
+ = +
( )( ) =(
6 22
3 31
3 21
3 3 3 2
58 000000037
5 8 10111. .
. )) ( ) =( ) ( ) = =
3 7 10
5 8 3 7 10 10
21 46 10 2 1
8
1 8
7
.
. .
. . 446 10
0000000046 82 000 000
4 6 10
6
9
( )( ) =( )
12. . , ,
. 88 2 10
4 6 8 2 10 10
37 72 10 3 772
7
9 7
2
.
. .
. .
( ) =( ) ( ) = =
( ) ( ) =( ) ( ) =
10
0000096 32
9 6 10 3 2 10
9
1
6 1
13. .
. .
.. .
..
6 3 2 10 10 3 10
0000012 18000
6 1 7 ( )( ) = ( )( )
14.000054
1 2 10 1 8 10
5 4 10
1 2 1 8 10
6 1
7
=
( ) ( )
=
( )
. .
.
. . 66 1
7
5
7
5
10
5 4 10
2 16 10
5 4 10
2 16 10
( )
=
=
( )
.
.
.
. 55 4 10
2 16 5 4 10 10
4 10 4 10
7
5 7
2 1
.
. .
.
( ) =( ) ( ) =
=
15. 9 2 6
9
2 1 2
3 2
2 3
3 4
2 1 1
X YZYX
XY Z
Z Y
X YZ
X Z
X Y ZY X
+ =
+ =
+
1 1 2 3 22 3
3 4
12
2 6
9 2 6
XY Z Z Y X YZ
X Z
XZ XYZ X YZ33
3 4
1 2 3 3 4
1
9 2 6
9 2 6
X Z
XZ XYZ X YZ X Z
XZ XYZ XYZ
=
+ =
+
=
=
( )
1
19 4 9 4
18
17
2
56 18
XZ XYZ or XZ XYZ
X X
XX
16.
556 17
56 2
568
567
112
7 8 1121 112
XX
X
XX
XX
X
XX
( ) = ( )
=
= =
=
( )( )( ) = ( )( )( ) =
1112
4 3 2 4 3 23 4 2 3 4 2
X
X Y X X X YX X17.
224 24
48 16 48
3 4 2
7 5 4 6 37 5
X Y XY
D E F E F D E F
+ ( )+
=
=18. 44
6 3
7 5 4
6 37 5 4 6 3
7 11
16
3 3
3
E F
D E F
E FD E F E F
D E F
=
= =
oor E F
D
X X
X X
X X
3
6 47
7 7 6 7 47
7 42 287
11
7
19. + =
( ) + ( ) = ( )
+ =
77 42 47 4 42
3 42423
14
X XX X
X
X
+ = =
=
= =
-
ALGEBRA 2
sYstEMAtic REViEW 4D - sYstEMAtic REViEW 4E
soLUtions 267
20. 3 24
5 82
8
4 3 24
4 5 4 82
4 8
4 3
X X
X X
+ = +
( ) + ( ) = ( ) + ( )
( ) XX X
X X
X
+( ) = ( ) +( )
+ =( ) +( )
24
20 4 82
32
3 2 20 2 81
32
3 188 2 16 323 2 16 32 18
2
= + = +
=
XX X
X
Systematic Review 4ESystematic Review 4E1. X X Y X X Y
X XY X
49 49
7 7
2 2 2 2= =
( ) = 22
4 6 11 6 4 11 6 15 6
5 6 5 6 30
Y
X Y X Y XY
2.
3.
+ = +( ) =( )( ) = ( )( ) =
44.
5.
6 7 4 6 6 7 4 6 6
42 4 36 42 4 6 42 24
10 63
7
1
+( ) = + =+ = + ( ) = +
= 00 91
10 3 30
128
8
161
4
200 100 2 10 2
13
72
= ( ) =
= =
= =
6.
7.
8. ( ) == =( ) =
= = =
( )( )
13
36 2
13
6 2 2 2
8
10
8 10
10 10
8 10
100
8 1010
9.
==
+ = + =
+ =
4 105
10
7
16
11
10 7
7 7
16 11
11 11
10 7
49
16 11
121
10.
110 77
16 1111
10 7 117 11
16 11 711 7
110 7 112
+ =
( )( ) =
( )( ) =
+ 11177
11. . .
. .
.
00034 00000026
3 4 10 2 6 10
3 4
4 7
( )( ) =( ) ( ) = ( ) ( ) =
( ) 2 6 10 10 8 84 10
77 000 740 000
4 7 11. .
, ,12. ,,
. .
. .
000
7 7 10 7 4 10
7 7 7 4 10 10
5
4 8
4 8
( ) =( ) ( ) =( ) ( ) =
66 98 10 5 698 10
490 000 007
4 9 10
12 13. .
, .
.
=
( ) ( ) =
13. 55 3
5 3
8 7
7 10
4 9 7 10 10
7 10 7 10
( ) ( ) =( )( ) =
=
.
.
14.228 000 000 210 000 000
98
2 8 10 2 1 107 8
, , , ,.
. .
( )( )=
( ) ( ))( )
=
( ) ( )( )
=
9 8 10
2 8 2 1 10 10
9 8 10
5 88
1
7 8
1
.
. .
.
. 110
9 8 10
5 88 10 9 8 10
5 88 9 8
15
1
15 1
.
. .
. .
=
( ) ( ) =( )
110 10
6 10 6 10
2 5
15 1
16 15
1 0 2
3 1 2
( ) = =
.
15. Q R t
t R Q
QQ R t
t R Q
Q R t
RRQ
Q R t t R Q Q
2 3 4
1 2 3
5 3 4
2
1 0 2 3 1 22
2 5
+ =
RR t
t R Q
Q R t
RRQ
Q R t Q R t t R
+ =
3 4
1 2 3
5 3 4
2
3 1 1 2 3 4 12 5 22 35 3 4
2
3 1 1 1 1 3 5 3 4 12 5
Q Q R t
RRQ
Q R t Q R t Q R t R R
+ =
+
=
+
+
1 2
3 1 1 1 3 3 4
3
3
2 5
2 5
Q
Q Rt Q R t Q Rt or
R
Q t
tQR
Q33 4
3 52
15
153
155
15 215
153
155
Rt
X X
X X
X X
16. =
( ) ( ) = ( )
==
==
= =
3015
5 3 22 2
22
1
X XX
X
-
ALGEBRA 2
sYstEMAtic REViEW 4E - LEsson PRActicE 5A-1
soLUtions268
17.
18.
7
7 1 7
1
3 2 2 2
3 2 2 2 5
AX Y X Y
AX Y X Y AX
( ) ( ) =( ) ( ) =
335 15
135
15
9
2 5 3 2 3
2 5 3
2 3
2 5 3
A B c A B
A B c
A B
A B c
=
=
AA B
A B c A B A B c or A B
c
X
=
=
=
2 3
2 5 3 2 3 4 8 34 8
39 9 9
38
19. 111 2
8 38
8 11 8 2
248
88 16
3 72723
24
( ) = ( ) ( )
=
=
= =
X
X
X
X
20.. 30 15 6 15
100 30 100 15 100 6 100 1
= ( ) ( ) = ( )
. .
. .
X X
X X 55
3 000 15 60 1 500
4 500 75
4 50075
60
( ) =
=
= =
, ,
,
,
X X
X
X
Lesson Practice 5A-1Lesson Practice 5A -1Remember that finding the soolution for a factoring
problem often involves trial and error. Review the
teaching material for if necessary. if you
have the blocks
tips
,, you may find them helpful.
ome problems may s bbe factored more than one way.
if you have a diifferent answer, it
check by multiplying
the faactors
X X
back to what you started with.
1. 2 7 1+ + 22 4 3
3 2 1 2
6 2
2
2
= +( ) +( )
+ + = +( ) +( )
+ = ( )
X X
X X X X
X X X
2.
3. XX
X X X X
X Y X Y X Y
+( )
+ = ( ) ( )
= ( ) +( )
3
11 30 6 52
2 2
4.
5.
6..
7.
8.
A A A
X X X X
X
2
2
2
81 9 9
2 3 2 3 1
3 17
= ( ) +( )
+ = +( ) ( )
+ XX X X
X X X X
X
+ = +( ) +( )
+ = ( ) +( )
+
10 3 2 5
5 14 3 5 1 3
4
2
2
9.
10. 221 5 4 1 5
2 12 16
2 6 8
2
2
2
X X X
X X
X X
+ = +( ) +( )
+ + =
( ) + +( ) =(
11.
)) +( ) +( )
+ + =
( ) + +( ) =( ) +( )
X X
X X X
X X X
X X X
2 4
6 9
6 9
3
3 2
2
12.
++( )381 9 9
3 3 9
XX
X X X X
X Y X Y X Y
+ = ( ) ( )
= ( ) +( )
3
11 30 6 52
2 2
4.
5.
6..
7.
8.
A A A
X X X X
X
2
2
2
81 9 9
2 3 2 3 1
3 17
= ( ) +( )
+ = +( ) ( )
+ XX X X
X X X X
X
+ = +( ) +( )
+ = ( ) +( )
+
10 3 2 5
5 14 3 5 1 3
4
2
2
9.
10. 221 5 4 1 5
2 12 16
2 6 8
2
2
2
X X X
X X
X X
+ = +( ) +( )
+ + =
( ) + +( ) =(
11.
)) +( ) +( )
+ + =
( ) + +( ) =( ) +( )
X X
X X X
X X X
X X X
2 4
6 9
6 9
3
3 2
2
12.
++( )
= ( ) +( ) =( ) +( ) +( )
3
81 9 9
3 3 9
4 2 2
2
13.
14.
A A A
A A A
X44 2 2 217 16 16 1
4 4 1 1
+ = ( ) ( ) =( ) +( ) ( ) +( )
X X X
X X X X
Forr this problem, it may help to express
X as Y 2 iin the first step. since X
would be eq
4 = X
X
2
4
2,
uual to Y so
After this
2,
.Y Y Y Y2 17 16 16 1 + = ( ) ( ) step, replace the Y with X and solve.2
15. 3 10 12 4
3 10 8 0
3 4 2 0
3 4 03
2
2
X X
X X
X X
XX
+ + =
+ + =
+( ) +( ) =
+ ===
=
+ + =
+ =
443
3 43
10 43
12 4
3 169
403
12 4
489
2
X
( ) ( )( ) + =
=
=
+ ==
( ) + ( ) +
1209
1089
4
369
4
4 4
2 02
3 2 10 22
ok
XX
112 4
3 4 20 12 412 20 12 4
4 4
=( ) + =
+ == ok
16. X
X X
XX
2
2
49 0
7 7 0
7 07
7 49 00
=
( ) +( ) =
==
( ) == 00
7 07
7 49 00 0
2
ok
XX
+ ==
( ) == ok
-
ALGEBRA 2
LEsson PRActicE 5A-1 - LEsson PRActicE 5A-2
soLUtions 269
17. 2 72
2 72 0
2 6 6 0
2 0
0
4 2
4 2
2
2
2
X X
X X
X X X
X
X
X
=
=
( ) +( ) =
=
=
= 00
2 0 72 0
2 0 72 0
0 0
6 06
4 2
( )
ok
( ) = ( )( ) =
=
==
XX ( )
2 6 72 6
2 1296 72 36
2592 2592
6 0
4 2( ) = ( )( ) =
=
+ =
ok
XX ==
( ) = ( )( ) =
=
62 6 72 6
2 1296 72 36
2592 2592
4 2
( )
ok
18. X X
X X
X X
X
4 2
4 2
2 2
26 27 2
26 25 0
1 25 0
1
+ =
+ =
( ) ( ) =( ) XX X X
X
+( ) ( ) +( ) =
= ( ) ( ) + = + =
1 5 5 0
1 1 26 1 27 21 26 27 2
2
4 2
==
= ( ) ( ) + = + =
=
=
2
1 1 26 1 27 21 26 27 2
2 2
4 2
ok
ok
X
X 55 5 26 5 27 2
625 650 27 22 2
5 5
4 2
4
( ) ( ) + = + =
=
= ( )
ok
X 226 5 27 2
625 650 27 22 2
2( ) + =
+ == ok
Lesson Practice 5A-2Lesson Practice 5A -21.
2.
X X X X
X
2
2
12 4 3
10
+ = +( ) ( )
XX X X
X X X X
X X
+ = ( ) ( )
= ( ) +( )
+ + =
24 4 6
8 9 9 1
7 10
2
2
3.
4. XX X
A B A B A B
or A B
+( ) +( )
= ( ) +( )(
5 2
25 25 5 5 5 5
25
2 25.
)) +( )
= ( ) +( )( ) ( ) = ( )
A B
X X X or
X X
6. 4 64 2 8 2 8
4 16 4
2
2 44 4
3 4 3
6 2 4 2
2 2
2
( ) +( )
+ + = +( ) +( )
= ( )
X
A AB B A B A B
X X
7.
8. 33 2
2 3 2 1
2 15 2 5 3
2
2
X X
X X
X X X X
( ) =( ) +( ) ( )
+ = ( ) +( )9.110.
Lesson Practice 5A -21.
2.
X X X X
X
2
2
12 4 3
10
+ = +( ) ( )
XX X X
X X X X
X X
+ = ( ) ( )
= ( ) +( )
+ + =
24 4 6
8 9 9 1
7 10
2
2
3.
4. XX X
A B A B A B
or A B
+( ) +( )
= ( ) +( )(
5 2
25 25 5 5 5 5
25
2 25.
)) +( )
= ( ) +( )( ) ( ) = ( )
A B
X X X or
X X
6. 4 64 2 8 2 8
4 16 4
2
2 44 4
3 4 3
6 2 4 2
2 2
2
( ) +( )
+ + = +( ) +( )
= ( )
X
A AB B A B A B
X X
7.
8. 33 2
2 3 2 1
2 15 2 5 3
2
2
X X
X X
X X X X
( ) =( ) +( ) ( )
+ = ( ) +( )9.110. 3 20 32 3 4 82X X X X+ = ( ) +( )
11.
12.
2 12 16 2 6 8
2 2 4
3 2 2X X X X X X
X X X
+ + = ( ) + +( ) =( ) +( ) +( )
33 21 18 3 7 6
3 1 6
1
2 2
8
A A A A
A A
X X
+ = ( ) +( ) =( ) ( ) ( )
=13. 44 4
2 2 4
2
1 1
1 1 1
1 1 1
( ) +( ) =( ) +( ) +( ) =( ) +( ) +(
X
X X X
X X X )) +( )X4 1
14. X X X X
X X X
4 2 2 2109 900 9 100
3 3 10
+ = ( ) ( ) =( ) +( ) ( ) XX
X X X
X X X
X X X
+( )
+ =
+ + =
+ + =
10
6 10 4
6 10 4 0
3 5 2 0
3 2
3 2
3 2
15.
XX X X
X X X
X
XX
X
( )3 5 2 0
3 2 1 0
0
3 2 03 2
2 + + =
+( ) +( ) =
=
+ ==
==
+ =
+ = 23
6 23
10 23
4 23
6 827
10 49
4
32( ) ( ) ( )
( ) ( ) ( + =
+ =
=
+ ==
23
4827
409
83
169
409
249
249
249
1 0
)
ok
XX 11
6 1 10 1 4 1
6 1 10 1 4
6
3 2 ( ) + ( ) =
( ) + =
( )
( )
++ ==
=
=
=
10 44 4
2 8 14 10
4 7 5
4 12 0
2
2
2
ok
X X
X X
X X
X
16.
( ) +( ) =
==
( ) ( ) =
6 2 0
6 06
2 6 8 6 14 10
2 3
2
X
XX
66 48 14 10
72 48 14 1010 10
2 02
2 2
( ) = =
=
+ ==
ok
XX
-
ALGEBRA 2
LEsson PRActicE 5A-2 - LEsson PRActicE 5B-1
soLUtions270
+ =
+ =
=
+ ==
23
4827
409
83
169
409
249
249
249
1 0
ok
XX 11
6 1 10 1 4 1
6 1 10 1 4
6
3 2 ( ) + ( ) =
( ) + =
( )
( )
++ ==
=
=
=
10 44 4
2 8 14 10
4 7 5
4 12 0
2
2
2
ok
X X
X X
X X
X
16.
( ) +( ) =
==
( ) ( ) =
6 2 0
6 06
2 6 8 6 14 10
2 3
2
X
XX
66 48 14 10
72 48 14 1010 10
2 02
2 2
( ) = =
=
+ ==
ok
XX
(( ) ( ) =( ) + =
+ ==
28 2 14 10
2 4 16 14 108 16 14 10
10 10 ok
117. X X X
X X
X X
X X X
3
3
2
50 50
100 0
100 0
10 10
=
=
=
( ) +( )( )
==
=
==
( ) =
0
0
10 010
10 50 10 50 10
1000
3( ) ( )
X
XX
==
+ ==
( )
500 500500 500
10 010
10 50 13
(
ok
XX
00 50 10
1000 500 500500 500
8 2
) ( )=
+ = =
=
ok
A18. 116 20
0 16 28
0 2 14
2 02
2
A
A A
A A
AA
+
= +
= ( ) ( )
==
= ( ) ( ) + = + =
=
8 2 16 2 208 4 32 208 8
14 0
2
ok
AAA =
= ( ) ( ) + = + =
148 14 16 14 208 196 224 208 8
2
ok
Lesson Practice 5B-1Lesson Practice 5B -11. 2
16
23
22 2
2X X X XX
X
+
++
+ =
+( )( ) +( )
+ ( )
( ) +( )+
+ =
+ +
1 26 1
1 23
22 4 6 6
2
2
XX
X X X XX X
X ++ +
+ = +
+ +
++
= +
X X X
X
X XXX
XX
XX
2
3
2
8 1
222
22
22
2 2
2. 111
22
1 21 2
2 22
2 22
=
+
( )
( )= +
( )
=
+ +
XX
XX
X XX
X XX
==
++
= +( )
+( )+
( )+( )( )
=
+ +
42
3 51
3 11
51
3 3
X
