﻿ 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 "a href="/properties/double-distributive-property.php">double distributive").

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

$$x \cdot x= x^2$$
$$x \cdot 9 =9x$$
$$7 \cdot x =7x$$
$$7 \cdot 9 = 63$$

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

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

### 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

### Practice Problems

##### Problem 1
Step 1

This is like example 1.

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

Step 2

 $$k^2$$ -4k 7k + (-28) k2+ 3k - 28
##### Problem 2
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

 k² -5k -3k + 15 k2 − 8k + 15
##### Problem 3
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

 6k² -8k 27k + (-36) 6k2+ 19k + -36
##### Problem 4
Step 1

This is like example 1 with the slight twist that you now have to deal with coefficients in form 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