the distributive property you will be able to use the distributive property you will be able to...
TRANSCRIPT
The Distributive The Distributive PropertyProperty
• You will be able to use the distributive property
•You will be able to simplify expressions with
like terms
The Distributive The Distributive PropertyPropertyThe product of a and
(b+c):
a(b+c) = ab + ac
ex: 5(x + 2) = 5x + 10
(b + c)a = ba + ca
ex: (x + 4)8 = 8x + 32
The product of a and (b-c):
a(b-c) = ab – ac
ex: 4(x –7)= 4x –28
(b-c)a = ba – ca
ex: (x-5)9 = 9x - 45
Sharing what is Outside the parentheses with
EVERYTHING INSIDE the parentheses.
What You Already What You Already Know…Know…You have been using this property in
a simplified form since third grade. Now we give it the algebraic term, and we extend it a bit.
18)6(3)24(3 OR
186122343
A Visual Example of the A Visual Example of the Distributive propertyDistributive property
Find the area of this rectangle.
We could say that this is 4(x + 2)
x +2
Or..
x 2
4
x 2
44
)2(44 x 84 x
So we can say that
4(x+2) = 4x+8
Example using the Example using the distributive propertydistributive property
)5(2 x )(2 x )5(2
102 x
Another Another ExampleExample
xx )4( xx)(
xx 42
)(4 x
)4(3 x )(3 x
123 x
Another Another ExampleExample
)4)(3(
)4)(5( y )4)(( y
204 y
Another Another ExampleExample
)5)(4(
Like TermsLike Terms
In a term that is the product of a number and a variable, the number is the coefficient of the variable.
23yx -1 is the coefficient of x
3 is the
coefficient of 2y
Like TermsLike Terms
Like terms are terms in an expression that have the same variable raised to the same power. In the expression above, 5x and –3x are like terms, but 5x and –x2 are not like terms. The constant terms –4 and2 are also like terms.
2)3()4(52 xxx
Like terms, Like terms, continued…continued…
The distributive property allows you to combine like terms that have variables by adding coefficients. An expression is simplified if it has no grouping symbols and if all the like terms have been combined.
Combining Like Combining Like TermsTerms
)4(23
24
3822
x
xx
xx