LESSON 1-7THE DISTRIBUTIVE PROPERTY

The distributive property is a way we can multiply (or divide) when the terms inside of the parentheses are not like terms.

3(2x + 3) means 3 groups of 2x + 3

GROUP 1 GROUP 3GROUP 2

To simplify, combine “like terms”(Put the “x”’s ( ) together and

the constants [numbers] ( ) together)

The result is 6x + 9

3(2x + 3) is the same as 3(2x) + 3(3)

6x + 9

To work a problem that involves the distributive property, multiply the value outside of the parentheses times each item inside of the parentheses. (It may be helpful to rewrite

everything in the parentheses so that it is an addition problem if there is subtraction involved.)

For example, -3(x – 2) would be rewritten as -3(x + –2 ).

After multiplying, combine like terms.

Simplify each expression using the distributive property

A.3(x + 8) = __________________ __________________

B. (5b – 4)(–7) = _________________ _________________ _________________

3(x) +

3x +

3(8)

24

(5b + – 4) (– 7)

(5b) (– 7) + (– 4)(– 7) – 35b +

28Use subtraction rules to rewrite

problem.

REWRITING FRACTION EXPRESSIONS:

Another way to think of this is each term is being divided by 5

Think of each term as being divided by 8.

Simplify the fractions

Because of the multiplicative identity, the 1 as a coefficient of x is not needed.

USING THE MULTIPLICATION PROPERTY OF –1 (REMEMBER –1 ● X = –X )

– (2y – 3x) = __________________

= _____________________

= ______________________

= ______________________

–1(2y + –3x)

–1(2y) +

–1(–3x)

–2y +

3xOR

3x – 2y

There is an understood“1” with the “–” sign.

– (–x + 31) = __________________

= ___________________

= ___________________

– 1 (–x + 31)

– 1 (–x) + (– 1)( 31)

x+ –31

x – 31 = ___________________

In an algebraic expression, a __________ is a

number, a variable, or the product of a number and

one or more variables. A _______________ is a

term that has no variable. A ________________ is

a numerical factor of a term.

_______ ___________ have the same variable

factors (raised to the same power).

term

constant

coefficient

Like terms

Like Terms? Why or why not?

7a & –3a _____________________

4x2 & 12x2 ____________________

6ab & –2a ____________________

xy2 & x2y _____________________

Yes, they both have the variable “a”

Yes, they both have the variable “x2”

No, the second term does not have a “b”

No, the 1st term has “y2” and the 2nd term has “x2”

COMBINING LIKE TERMS:

8x2 + 2x2 = __________________

= __________________

5x – 3 – 3x + 6y + 4 = ____________________ = __________________________ = __________________________

(8 + 2) (x2)10x2

It’s okay to just add the coefficients of the like terms.

5x + – 3 + – 3x + 6y + 4(5x + – 3x) + 6y + (4+ –

3) 2x + 6y + 1

Change subtraction to addition

Group like terms togetherSimplify

For a video explanation go to:Pearson Success Net Virtual Nerd for Lesson 1-7

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