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Lesson 1-7 The Distributive Property

Lesson 1-7 The 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 2. GROUP 3. To simplify, combine “like terms”

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Lesson 1-7 The Distributive Property

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  1. Lesson 1-7The Distributive Property

  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 2 GROUP 3

  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 3(x) + 3(8) 3(x + 8) = __________________ __________________ B. (5b – 4)(–7) = _________________ _________________ _________________ 3x + 24 (5b + – 4) (– 7) (5b) (– 7) + (– 4)(– 7) Use subtraction rules to rewrite problem. – 35b + 28

  6. Rewriting Fraction Expressions: 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. Using the Multiplication Property of –1 (Remember –1 ● x = –x ) –1(2y + –3x) – (2y – 3x) = __________________ = _____________________ = ______________________ = ______________________ There is an understood “1” with the “–” sign. –1(2y) + –1(–3x) –2y + 3x OR 3x – 2y

  9. – 1 (–x + 31) – (–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 _____________________ 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”

  12. Combining Like Terms: It’s okay to just add the coefficients of the like terms. (8 + 2) (x2) 8x2 + 2x2= __________________ = __________________ 5x – 3 – 3x + 6y + 4 = ____________________ = __________________________ = __________________________ 10x2 Change subtraction to addition 5x + – 3 + – 3x + 6y + 4 (5x + – 3x) + 6y + (4+ – 3) Group like terms together 2x + 6y + 1 Simplify

  13. 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.

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