# Multiplying Binomials

## Presentation on theme: "Multiplying Binomials"— Presentation transcript:

Multiplying Binomials
Distributive Property of Multiplication and the FOIL Method

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.

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

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

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

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

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

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

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

Your turn (with addition): (n+7)(2n+5) (n+7)(2n+5) = 2n2 + 5n + 14n + 35 = 2n2 + 19n + 35
Outer Inner First Last

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

Outer Outer Inner First Last Outer Inner First Last