**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:

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**

**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**

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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