1. L ESSON 1-7 T HE D ISTRIBUTIVE P ROPERTY

2. 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

3. 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

4. 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.

5. 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 +28 Use subtraction rules to rewrite problem.

6. R EWRITING F RACTION E XPRESSIONS : Another way to think of this is each term is being divided by 5

7. 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.

8. U SING THE M ULTIPLICATION P ROPERTY OF – 1 (R EMEMBER – 1 ● X = – X ) – (2y – 3x) = __________________ = _____________________ = ______________________ – 1(2y + – 3x) – 1(2y) + – 1( – 3x) – 2y +3x OR 3x – 2y There is an understood “1” with the “–” sign.

9. – (–x + 31) = __________________ = ___________________ – 1 (–x + 31) – 1 (–x) + (– 1)( 31) x + – 31 x – 31= ___________________

10. 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

11. Like Terms? Why or why not? 7a & –3a _____________________ 4x 2 & 12x 2 ____________________ 6ab & –2a ____________________ xy 2 & x 2 y _____________________ Yes, they both have the variable “a” Yes, they both have the variable “x 2 ” No, the second term does not have a “b” No, the 1 st term has “y 2 ” and the 2 nd term has “x 2 ”

12. C OMBINING L IKE T ERMS : 8x 2 + 2x 2 = __________________ = __________________ 5x – 3 – 3x + 6y + 4 = ____________________ = __________________________ (8 + 2) (x 2 ) 10x 2 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 together Simplify

15. For a video explanation go to: Pearson Success Net Virtual Nerd for Lesson 1-7 You may have to be logged in to your Pearson (textbook) account to view this, but try anyway.