1 Press Ctrl-A ©G Dear 2008 – Not to be sold/Free to use Binomial Products Stage 6 - Year 11...
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1 Press Ctrl-A Press Ctrl-A ©G Dear 2008 – Not to be sold/Free to use Binomial Products Binomial Products Stage 6 - Year 11 Stage 6 - Year 11 Mathematic (Preliminary)
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Transcript of 1 Press Ctrl-A ©G Dear 2008 – Not to be sold/Free to use Binomial Products Stage 6 - Year 11...
1Press Ctrl-APress Ctrl-A
©G Dear 2008 – Not to be sold/Free to use
Binomial ProductsBinomial ProductsStage 6 - Year 11Stage 6 - Year 11
Mathematic(Preliminary)
2
Binomial Products
FOIL Method
(a + b)(x + y) =
Firsts, Outers, Inners, Lasts.
3
Binomial Products
FOIL Method
(a + b)(x + y) =
Firsts, Outers, Inners, Lasts.
ax
4
Binomial Products
FOIL Method
(a + b)(x + y) =
Firsts, Outers, Inners, Lasts.
ax+ ay
5
Binomial Products
FOIL Method
(a + b)(x + y) =
Firsts, Outers, Inners, Lasts.
ax+ ay
+ bx
6
Binomial Products
FOIL Method
(a + b)(x + y) =
Firsts, Outers, Inners, Lasts.
ax+ ay
+ bx
+ by
7
Binomial Products
FOIL Method
(a + b)(x + y) =
Firsts, Outers, Inners, Lasts.
or Distributive Method(a + b)(x + y) =
ax+ ay + bx
+ by
8
Binomial Products
FOIL Method
(a + b)(x + y) =
Firsts, Outers, Inners, Lasts.
or Distributive Method(a + b)(x + y) =
ax+ ay
+ bx
+ by
a(x + y)
9
Binomial Products
FOIL Method
(a + b)(x + y) =
Firsts, Outers, Inners, Lasts.
or Distributive Method(a + b)(x + y) =
ax+ ay + bx
+ by
+ b(x + y)a(x + y)
10
Binomial Products
FOIL Method
(a + b)(x + y) =
Firsts, Outers, Inners, Lasts.
or Distributive Method(a + b)(x + y) = = ax + ay + bx +
by
ax+ ay + bx
+ by
+ b(x + y)a(x + y)
11
Binomial Products
Examples of Distributive Law
(2x + 3)(3x + 2) =
2x(3x + 2)+ 3(3x +
2)= 6x2
+
4x+ 9x +
6= 6x2
+ 13x
+ 6
12
Binomial Products
Examples of Distributive Law
(x - 5)(2x - 3) = x(2x -
3)- 5(2x - 3)
= 2x2 -
3x- 10x +
15 Common Mistake
= 2x2 - 13x +
15
13
Binomial Products
Related Products
(a + b)(x + y + z) =
ax + ay + az
+ bx + by + bz
(2x +3)(x + y - 2) = = 2x2 + 2xy - 4x + 3x + 3y -
6= 2x2 + 2xy - x + 3y - 6
= 2x(x + y - 2)
+ 3(x + y - 2)
Example
14
Binomial Products
Special Products
(a + b)2 =
a2 + 2ab +
b2
Proof
(a + b)2 =
(a + b)(a + b)
= a(a + b)
+ b(a + b)= a2 + ab+ ab + b2
= a2 + 2ab + b2
15
Binomial Products
Special Products
(a + b)2 =
a2 + 2ab +
b2
Example
(2x + 3)2 =
(2x)2 + 2 x 2x x 3 + 32
= 4x2 + 12x + 9
a
b
16
Binomial Products
Special Products
(a - b)2 =
a2 - 2ab + b2
Proof
(a - b)2 =
(a - b)(a - b)
= a(a - b)
- b(a + b)= a2 - ab - ab + b2
= a2 - 2ab + b2
17
Binomial Products
Special Products
(a - b)2 =
a2 - 2ab + b2
Example
(3x - 2)2 =(3x)2 - 2 x 3x x 2 + 22
= 9x2 - 12x + 4
a
b
18
Binomial Products
Special Products
(a + b)(a -b) =
a2 - b2
Proof
(a + b)(a - b) =
= a(a - b)
+ b(a - b)= a2 - ab + ab - b2
= a2 - b2
19
Binomial Products
Special Products
(a + b)(a -b) =
a2 - b2
Example
(2x + 3y)(2x - 3y) =
= 4x2 - 9y2
a
b
(2x)2 - (3y)2
a
b
