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Updated on Oct 9, 2013

## What is FOIL?

The FOIL Method — First Outer Inner Last — is the best system to use when multiplying two binomials. You can think of it as a slightly more advanced version of the distributive property of multiplication, which tells us that a(b + c) = ab + ac.

When multiplying (a+b)(c+d), for example, FOIL reminds us that we must distribute both the a and the b across the c and the d. Each part of the first binomial must be multiplied by each of the parts of the second binomial. Then, we add all of the partial products together.

## What is a binomial?

A binomial is an algebraic expression that consists of the sum or the difference of two terms, for example:

• 2 + x
• x + y
• 3a + 5b
• xy – ab
• 3x3 – 2y4

## When to use the FOIL method

Whenever you need to multiply two binomials!

## How to use the FOIL method

Example 1

F      O     I     L

(a+b)(c+d) = ac + ad + bc + bd

There are four partial products that must be added together:

1. The product of the First terms of each binomial (a and c)
2. The product of the “Outer” terms (a and d)
3. The product of the “Inner” terms (b and c)
4. The product of the Last terms (b and d)

Example 2

(x-4)(x+3)

• First: x × x = x2
• Outer: x × 3 = 3x
• Inner: -4 × x = -4x
• Last: -4 × 3 = -12

x2 + 3x – 4x – 12

x2 -1x -12

Example 3

(a-b)(c-d)

• First: a× c = ac
• Outer: a× -d = -ad
• Inner: -b × c = -bc
• Last: -b × -d = +bd

ac – ad – bc + bd

Example 4

(x2-y)(y2+x)

• First: x2 × y2 = x2y2
• Outer: x2 × x = x3
• Inner: -y × y2 = -y3
• Last: -y × x = -yx

x2y2 + x3 – y3 – yx

TRY THESE!

1. (6 + a)(a – 2)
2. (5x2-a)(5x2+a)
3. (d + e/2)(-a – 1)
4. (3s4-t2)(2s3+t3)

1. 6a -12 + a2 – 2a                Simplify: a2 + 4a - 12
2. 25x4 + 5ax2 - 5ax2 – a2     Simplify: 25x4 – a2
3. –ad – d – ea/2 – e/2
4. 6s7 + 3s4t3 – 2s3t2 – t5

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