Foil Method to Multiply Binomials

Video Tutorial on How to Multiply Binomials

The FOIL 'formula' is a way to multiply binomials. "FOIL" is an acronym to remember a set of rules to perform this multiplication. To FOIL you multiply together each of the following below

• F: Firsts
• O: Outer
• I: Inner
• L: Lasts

and then you add each of these products as demonstrated in the examples below.

Example 1 Let's multiply the following binomials:

(X + 3 )( X + 2)

Step 1) Multiply the first, outer, inner and last pairs

First: x • x = x² Outer: x • 2 = 2x Inner: 3 • x = 3x Last: 3 • 2 = 6

Step 2) Simplify by adding the terms

x²   2x   3x + 6   x2+ 5x + 6

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Problem 1) Multiply the 2 binomials below:

(k + 7 )( k - 4)

Step 1

This is like example 1 .

Step 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

Step 2) Simplify by adding the terms

k²   -4k   7k + -28   k2+ 3k - 28

Problem 2) Multiply the following binomials:

(k - 3 )( k - 5)

Step 1

This is like example 1 .

Step 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

Step 2) Simplify by adding the terms

k²   -5k   -3k + 15   k2 − 8k + 15

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Problem 3) Multiply the binomials:

(2k + 9)(3k - 4)

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.

Step 1) 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

Step 2) Simplify by adding the terms

6k²   -8k   27k + -36   6k2+ 19k + -36

Problem 4) Multiply the 2 binomial :below :

(5k - 1 )(2k + 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.

Step 1) 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

Step 2) Simplify by adding the terms

10k²   15k   -2k + -3   10k2+ 13k + -3