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Distributive Property

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O To distribute and get rid of the parenthesis, simply multiply the number on the outside by the terms on the inside of the parenthesis.

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Simplifying by Using the Distributive Property Sometimes you may need to use the Distributive Property to simplify an algebraic expression. The Distributive Property states: a(b + c) = ab + ac

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Simplifying by Using the Distributive Property To distribute and get rid of the parentheses, simply multiply the number on the outside by the terms on the inside of the parentheses. 2(x + 5) = "two times the quantity of x plus five"

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Simplifying by Using the Distributive Property To distribute and get rid of the parentheses, simply multiply the number on the outside by the terms on the inside of the parentheses. 2(x + 5) = 2x

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Simplifying by Using the Distributive Property To distribute and get rid of the parentheses, simply multiply the number on the outside by the terms on the inside of the parentheses. 2(x + 5) = 2x + 10

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We Do! 3(a - 9)-4(2x - 8)

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We Do! 3(a - 9)-4(2x - 8)

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We Do! 3(a - 9) 3a + (-27) 3a - 27 -8x + 32 3(a - 9)-4(2x - 8) -4(2x + (-8)) 3(a + (-9))

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Distributing After Subtraction When you distribute after subtraction, you must distribute the negative. 8c - 3(c - 5) =

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Distributing After Subtraction When you distribute after subtraction, you must distribute the negative. 8c - 3(c - 5) =

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Distributing After Subtraction When you distribute after subtraction, you must distribute the negative. 8c - 3(c - 5) = 8c -3c + 15

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Distributing After Subtraction When you distribute after subtraction, you must distribute the negative. 8c - 3(c - 5) = 8c -3c + 15 Then combine like terms! 8c - 3c + 15 = 5c + 15

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We Do! 16 - 4(c + 3)3 - 5(a - 4)

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We Do! 16 - 4(c + 3)3 - 5(a - 4)

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We Do! 16 - 4(c + 3) 16 - 4c - 12 4 - 4c 3 - 5(a - 4) 3 - 5a + 20 23 - 5a

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Distributing After Subtraction 8) 16 – 4(c + 3) 9) 3 – 5(a – 4) When you distribute after subtraction, you must distribute the minus sign as part of the number being distributed. You Try

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Distributing When No Number is Present Outside the Parentheses Sometimes you will come across an algebraic expression in which you will need to distribute in order to clear the parentheses, but there is no number there! - (6x + 4) =

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Distributing When No Number is Present Outside the Parentheses In this case, you are looking for the opposite of the quantity 6x + 4. To find this you can add a 1 and distribute -1. - 1(6x + 4) =

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Distributing When No Number is Present Outside the Parentheses In this case, you are looking for the opposite of the quantity 6x + 4. To find this you can add a 1 and distribute -1. - 1(6x + 4) = -6x - 4

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We Do! - (5x - 9)- (2b + 6)

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We Do! -1(5x - 9)-1(2b + 6)

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We Do! -1(5x - 9) -5x + 9 -1(2b + 6) -2b - 6

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Distributing Examples No Number Outside Parenthesis 5) - (5x – 9) 6) - (2b + 6) To do this, add a 1 before the parenthesis and distribute -1. You Try

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Simplifying Algebraic Expressions: Overview When you are simplifying algebraic expressions, you should do so in the following order: 1. Distribute to clear the parentheses 2. Combine like terms

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Put It All Together! Try These: 4(b + 8) - 7b4x - 8(2x + 3)

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Put It All Together! Try These: 4(b + 8) - 7b 4b + 32 - 7b -3b + 32 4x - 8(2x + 3) 4x - 16x - 24 -12x - 24

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Practice Distributive Property 1)8(x + 4) 2)4(12 + 2x) 3)x(6 + 5) 4)5 – 3(8x + 2) 5)7(3x + 6) – 2

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