Multiplying Binomial × Binomial

• An important skill in algebra is to multiply a binomial times a binomial. This type of problem will come up often.

( 5) 3x x • Example

1:Multiply the binomials:

Use the distributive property, distributing the first binomial.

( ) 35x x

( 5)x x ( 5) 3x

Distribute again …

( 5)x x ( 5) 3x

( 5) (3 5)x xx

5 3 3 5x x x x 2 5 3 15x x x

2 8 15x x

Combine like terms …

( 5) 3x x • Example

2:Multiply the binomials:

( ) 35x x

xx

Let’s work the same problem again, but use a simpler method, which is to distribute the terms of the first binomial

3x 5 x 35 2 3 5 15x x x

2 3 5 15x x x

2 8 15x x

Combine like terms …

This is the same answer we got last time!

( ) 35x x

Look at the multiplication process again:

1) First terms

2) Outside terms

3) Inside terms

4) Last terms

x x

3x

5 x

5 3

The pattern spells FOIL, which we will use as a memory tool.

(2 3) 4x x

• Example 3:Use FOIL to multiply the binomials:

1) First terms

2) Outside terms

3) Inside terms

4) Last terms

2x x ( 3) x 2 4x 3 4

We want to get good at using FOIL, doing the work quickly in our head.

2x x ( 3) x 2 4x 3 4

22 8 3 12x x x

22 5 12x x

(5 4) 3 7x x

• Example 4:Use FOIL to multiply the binomials:

1) First terms

2) Outside terms

3) Inside terms

4) Last terms

215x 12x35x 28

215 47 28x x