the distributive property you will be able to use the distributive property you will be able to...

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The Distributive The Distributive Property Property You will be able to use the distributive property You will be able to simplify expressions with like terms

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Page 1: The Distributive Property You will be able to use the distributive property You will be able to simplify expressions with like terms

The Distributive The Distributive PropertyProperty

• You will be able to use the distributive property

•You will be able to simplify expressions with

like terms

Page 2: The Distributive Property 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.

Page 3: The Distributive Property You will be able to use the distributive property You will be able to simplify expressions with like terms

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

Page 4: The Distributive Property You will be able to use the distributive property You will be able to simplify expressions with like terms

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

Page 5: The Distributive Property You will be able to use the distributive property You will be able to simplify expressions with like terms

x 2

44

)2(44 x 84 x

So we can say that

4(x+2) = 4x+8

Page 6: The Distributive Property You will be able to use the distributive property You will be able to simplify expressions with like terms

Example using the Example using the distributive propertydistributive property

)5(2 x )(2 x )5(2

102 x

Page 7: The Distributive Property You will be able to use the distributive property You will be able to simplify expressions with like terms

Another Another ExampleExample

xx )4( xx)(

xx 42

)(4 x

Page 8: The Distributive Property You will be able to use the distributive property You will be able to simplify expressions with like terms

)4(3 x )(3 x

123 x

Another Another ExampleExample

)4)(3(

Page 9: The Distributive Property You will be able to use the distributive property You will be able to simplify expressions with like terms

)4)(5( y )4)(( y

204 y

Another Another ExampleExample

)5)(4(

Page 10: The Distributive Property You will be able to use the distributive property You will be able to simplify expressions with like terms

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

Page 11: The Distributive Property You will be able to use the distributive property You will be able to simplify expressions with like terms

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

Page 12: The Distributive Property You will be able to use the distributive property You will be able to simplify expressions with like terms

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.

Page 13: The Distributive Property You will be able to use the distributive property You will be able to simplify expressions with like terms

Combining Like Combining Like TermsTerms

)4(23

24

3822

x

xx

xx