Multiplying BinomialsDistributive Property of Multiplication and

the FOIL Method

Primary Objective: To find the product of two binomials

Secondary Objective: To review the Distributive Property of Multiplication and to learn the FOIL Method.

Objectives

a(b+c) = a(b+c) = ab + acor

(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 addition)

a(b-c) = a(b-c) = ab-acor

(b-c)a = (b-c)a = ba-ca

Again, per the Commutative Property, ab-ac = ba-ca

Distributive Property of Multiplication (with respect to subtraction)

(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

The Distributive Property Works for Two Binomials

(a+b) (c+d) =

ac + ad + bc + bd First Outer Inner Last Terms Terms Terms Terms

This is called the FOIL Method

FOIL Method

Outer

Inner

First

Last

Learn the FOIL Methodbut remember that you are

using the

DISTRIBUTIVE PROPERTY

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

(2x+5)(3x+4)

(2x+5)(3x+4)

6x2 + 8x + 15x + 20 = First Outer Inner Last

combine like terms6x2 + 23x + 20

OuterInner

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 terms9h2 + 12h - 5

OuterInner

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

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