﻿ Foil method to multiply binomials, example, practice problem and tutorial

# Examples and practice with formula

## What "FOIL" stands for

"Foil" is a way that people remember the 'formula' for multiplying binomials. (An alternative approach is to use "double distributive" )

FOIL stands for first, outer, inner and last pairs . You are supposed to multiply these pairs as shown below!

 Firsts : $$x \cdot x= x^2$$ Outers : $$x \cdot 9 =9x$$ Inners : $$7 \cdot x =7x$$ Lasts : $$7 \cdot 9 = 63$$

#### So, now that we've multiplied, what is next?

Add up each term!

 $$x^2$$ 9x 7x + 63 $$x^2 + 16x + 63$$

### Visualizing with Rectangles and Area

#### What is the area of the rectangle below?

The area of each part of the rectangle can be seen as a 'part' of the FOIL formula

##### Example 1

Let's multiply the following binomials: (X + 3 )( X + 2)

Step 1

First: x • x = $$x^2$$
Outer: x • 2 = 2x
Inner: 3 • x = 3x
Last: 3 • 2 = 6

Step 2
 $$x^2$$ 2x 3x + 6 x2+ 5x + 6

### Practice Problems

Step 1

This is like example 1

Multiply the first, outer, inner and last pairs

First: k • k = k²
Outer: k • -4 = -4k
Inner: 7 • k = 7k
Last: 7 • -4 = -28

Step 2

Simplify by adding the terms

 $$k^2$$ -4k 7k + (-28) k2+ 3k - 28
Step 1

This is like example 1

Multiply the first, outer, inner and last pairs

First: k • k = k²
Outer: k • -5 = -5k
Inner: -3 • k = -3k
Last: -3 • -5 = 15

Step 2

Simplify by adding the terms

 k² -5k -3k + 15 k2 − 8k + 15
Step 1

This is like example 1 with the slight twist that you now have to deal with coefficients in from of the variable of each binomial.

Multiply the first, outer, inner and last pairs

First: 2k • 3k = 6k²
Outer: 2k • -4 = -8k
Inner: 9 • 3 k = 27k
Last: 9 • -4 = -36

Step 2

Simplify by adding the terms

 6k² -8k 27k + (-36) 6k2+ 19k + -36
Step 1

This is like example 1 with the slight twist that you now have to deal with coefficients in from of the variable of each binomial.

Multiply the first, outer, inner and last pairs

First: 5k • 2k = 10k²
Outer: 5k • 3 = 15k
Inner: -1 • 2k = -2k
Last: -1 • 3 = -3

Step 2

Simplify by adding the terms

 10k² 15k -2k + (-3) 10k2+ 13k + -3

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