1. Multiplying Binomials
Distributive Property of Multiplication and the FOIL Method

2. 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.

3. 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

4. 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

5. 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

6. 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

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

8. 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

9. 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

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

11. 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

12. Outer
Outer
Inner
First
Last
Outer
Inner
First
Last