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Multiplication of Two Binomials Help

based on 3 ratings
By — McGraw-Hill Professional
Updated on Sep 8, 2011

Multiplication of Two Binomials

In algebra, there are some special products that you will need to know. The first one is to be able to find the product of two binomials. In order to do this, you can use the distributive law twice.

Examples

Example 1

Multiply (x + 4) (x + 2).

Solution 1

Distribute (x + 4) over (x + 2) as shown:

(x + 4)(x + 2) = (x + 4)x + (x + 4)2.

Next distribute each point as shown:

Multiplication of Two Binomials

Then combine like terms:

= x 2 + 6x +8

Hence, (x + 4)(x + 2) = x 2 + 6x + 8

Example 2

Multiply (3x + 1)(x - 2).

Solution 2

Multiplication of Two Binomials

FOIL Method for Multiplying Two Binomials

A shortcut method for multiplying two binomials is called the FOIL method. FOIL stands for:

F = First

O = Outer

I = Inner

L = Last

Example 3

Multiply (x - 7)(x + 2) using the FOIL method.

Solution 3

Multiplication of Two Binomials

Combine the like terms:

2x - 7x = -5x

Hence, (x - 7)(x + 2)= x 2 - 5x - 14.

Multiplication of Two Binomials  Practice Problems

Practice

Multiply:

1. (x + 6)(x + 7)

2. (x - 4)(x - 6)

3. (x + 9)(x - 11)

4. (x - 3)(x + 3)

5. (x + 4)(x + 4)

Answers

1. x 2 + 13x + 42

2. x 2 - 10x + 24

3. x 2 - 2x - 99

4. x 2 - 9

5. x 2 + 8x + 16

Practice problems for these concepts can be found at: Operations With Monomials And Polynomials Practice Test.

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