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**Multiplying Binomials**

Distributive Property of Multiplication and the FOIL Method

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Objectives Primary Objective: To find the product of two binomials Secondary Objective: To review the Distributive Property of Multiplication and to learn the FOIL Method.

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**Distributive Property of Multiplication (with respect to addition)**

a(b+c) = a(b+c) = ab + ac or (b+c)a = (b+c)a = ba + ca What property tell us that both results are the same (i.e. that ab + ac = ba + ca)? The Commutative Property

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**Distributive Property of Multiplication (with respect to subtraction)**

a(b-c) = a(b-c) = ab-ac or (b-c)a = (b-c)a = ba-ca Again, per the Commutative Property, ab-ac = ba-ca

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**The Distributive Property Works for Two Binomials**

(a+b)(c+d) First distribute the multiplication of a to c and d , then distribute the multiplication of b to c and d. (a+b)(c+d) = ac + ad + bc + bd

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FOIL Method (a+b) (c+d) = ac + ad + bc + bd First Outer Inner Last Terms Terms Terms Terms This is called the FOIL Method Outer Inner First Last

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**but remember that you are using the DISTRIBUTIVE PROPERTY**

Learn the FOIL Method but remember that you are using the DISTRIBUTIVE PROPERTY

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**Example 1: Distributive Property of Multiplication (with respect to addition)**

(2x+5)(3x+4) 6x2 + 8x + 15x + 20 = First Outer Inner Last combine like terms 6x2 + 23x + 20 Outer Inner First Last

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**Example 2: Distributive Property of Multiplication (with respect to subtraction)**

(3h+5)(3h-1) (3h+5) (3h-1) 9h2 - 3h + 15h - 5 = First Outer Inner Last combine like terms 9h2 + 12h - 5 Outer Inner First Last

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**Your turn (with addition): (n+7)(2n+5) (n+7)(2n+5) = 2n2 + 5n + 14n + 35 = 2n2 + 19n + 35 **

Outer Inner First Last

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**Hint: draw line through “z” so you don’t confuse with “2”**

Your turn (with subtraction): (z+4)(z-7) (z+4) (z-7) = z2 – 7z + 4z - 28 = z2 - 3z – 28 Hint: draw line through “z” so you don’t confuse with “2” Outer Inner First Last

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Outer Outer Inner First Last Outer Inner First Last

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