# Multiplying Binomials

Binomials are the sum or difference of two terms in an algebraic expression. Here you learn how to multiply them using FOIL method.

## Step by step guide to Multiplying Binomials

• The sum or the difference of two terms in an algebraic expression is a binomial.
• Use “FOIL” (First–Out–In–Last) to multiply Binomials.
$$\color{blue}{(x+a)(x+b)=x^2+(b+a)x+ab}$$

### Example 1:

Multiply Binomials. $$(x+3)(x-2)=$$

Solution:

Use “FOIL”. (First–Out–In–Last): $$(x+3)(x-2)=x^2−2x+3x−6$$
Then simplify: $$x^2−2x+3x−6=x^2+x−6$$

### Example 2:

Multiply Binomials. $$(x-4)(x-2)=$$

Solution:

Use “FOIL”. (First–Out–In–Last):
$$(x-4)(x-2)=x^2-2x-4x+8$$
Then simplify: $$x^2-6x+8$$

### Example 3:

Multiply Binomials. $$(x-2)(x+2)=$$

Solution:

Use “FOIL”. (First–Out–In–Last):
$$(x-2)(x+2)=x^2+2x-2x-4$$
Then simplify: $$x^2+2x-2x-4=x^2-4$$

### Example 4:

Multiply Binomials. $$(x+5)(x-2)=$$

Solution:

Use “FOIL”. (First–Out–In–Last):
$$(x+5)(x-2)=x^2-2x+5x-10$$
Then simplify: $$x^2-2x+5x-10=x^2+3x-10$$

## Exercises

### Multiply.

1. $$\color{blue}{ (3x – 2) (4x + 2)}$$
2. $$\color{blue}{(2x – 5) (x + 7)}$$
3. $$\color{blue}{ (x + 2) (x + 8)}$$
4. $$\color{blue}{ (x^2 + 2) (x^2 – 2)}$$
5. $$\color{blue}{ (x – 2) (x + 4)}$$
6. $$\color{blue}{ (x – 8) (2x + 8)}$$

1. $$\color{blue}{12x^2 – 2x – 4 }$$
2. $$\color{blue}{2x^2 + 9x – 35 }$$
3. $$\color{blue}{ x^2 + 10x + 16}$$
4. $$\color{blue}{x^4 – 4 }$$
5. $$\color{blue}{x^2 + 2x – 8 }$$
6. $$\color{blue}{2x^2 – 8x – 64 }$$