The Distributive Property The process of distributing the number on the outside of the parentheses...
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The Distributive Property The process of distributing the number on the outside of the parentheses to each term on the inside. a(b + c) = ab + ac a(b - c) = ab - ac Example #1 5(x + 7) 5 • x + 5 • 7 5x + 35
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Transcript of The Distributive Property The process of distributing the number on the outside of the parentheses...
The Distributive PropertyThe process of distributing the number
on the outside of the parentheses to each term on the inside.a(b + c) = ab + ac a(b - c) = ab - ac
Example #1
5(x + 7)
5 • x + 5 • 7
5x + 35
Example using the distributive Example using the distributive propertyproperty
)5(2 x )(2 x )5(2
102 x
Another ExampleAnother Example
xx )4( xx)(
xx 42
)(4 x
)4(3 x )(3 x
123 x
Another ExampleAnother Example
)4)(3(
)4)(5( y )4)(( y
204 y
Another ExampleAnother Example
)5)(4(
Example #2
3(m - 4)3 • m - 3 • 4
3m - 12
Example #3
-2(y + 3)-2 • y + (-2) • 3
-2y + (-6)-2y - 6
Which statement demonstrates the distributive property incorrectly?
1. 3(x + y + z) = 3x + 3y + 3z
2. (a + b) c = ac + bc
3. 5(2 + 3x) = 10 + 3x
4. 6(3k - 4) = 18k - 24
Answer Now
A term is a1) number,
2) variable, or
3) a product / quotient of numbers and variables.
Example
5
m
2x2
The coefficient isthe numerical part of the term.
Examples
1) 4a
4
2) y2
1
3) 5x2
7 5
7
Like Terms are terms with the same variable AND exponent.
To simplify expressions with like terms, simply combine the like terms.
Are these like terms?
1) 13k, 22k
Yes, the variables are the same.
2) 5ab, 4ba
Yes, the order of the variables doesn’t matter.
3) x3y, xy3
No, the exponents are on different variables.
Combining Like Combining Like TermsTerms
)4(23
24
3822
x
xx
xx
Which of the following is the simplified form of
-4x + 7x ?1. -4
2. 3x
3. -3x
4. 4
Answer Now
8x 2 2x2 5a a
The above expression simplifies to:
10x2 6a
8x 2 2x2
5a and a are like terms
and are like terms
12a
2) 6.1y - 3.2y
2.9y
3) 4x2y + x2y
5x2y
4) 3m2n + 10mn2 + 7m2n - 4mn2
10m2n + 6mn2
Simplify Expressions1) 5a + 7a
21a + 6b
6) 4d + 6a2 - d + 12a2
18a2 + 3d
3y
4
y
47)
3y
4
1y
4
4y
41y
y
5) 13a + 8a + 6b
Which of the following is the simplified form of
5x - 4 - 7x + 14 ?
Answer Now
1. -12x + 10
2. -2x + 10
3. 2x - 18
4. 12x – 18
If a triangle has sides 3x - 2, 5 - x and 2x - 5, what is the perimeter of the triangle?
Answer Now
1. 4x - 2
2. 4x + 2
3. 5x - 2
4. 5x - 7
Which figure below models the simplification of - 4x - 5 + 7x + 7 using these tiles?
Answer Now
1.
2.
3.
4.
Bonus! Which of the following is the simplified form of a + 3a - 4(9 - a) ?
Answer Now
1. -36
2. 3a - 36
3. 8a - 36
4. 8a + 36
