Pre-Algebra Demystified

SOLUTION

Distribute (xþ4) over (xþ2) as shown:

ðxþ 4 Þðxþ 2 Þ¼ðxþ 4 Þxþðxþ 4 Þ 2 :

Next distribute each point as shown:

¼xxþ 4 xþx 2 þ 4  2

¼x^2 þ4xþ2xþ 8

Then combine like terms:

¼x^2 þ6xþ 8

Hence, (xþ4)(xþ2)¼x^2 þ6xþ 8

EXAMPLE
Multiply (3xþ1)(x
2).

SOLUTION

ð3xþ 1 Þðx
 2 Þ¼ð3xþ 1 Þxþð3xþ 1 Þð
 2 Þ

¼3xxþ 1 xþ3xð
 2 Þþ 1 ð
 2 Þ

¼3x^2 þx
6x
 2

¼3x^2 
5x
 2

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

F¼First

O¼Outer

I¼Inner

L¼Last

EXAMPLE
Multiply (x
7)(xþ2) using the FOIL method.

SOLUTION

First xx¼x^2

Outer x 2 ¼2x

Inner 
 7 x¼
7x

Last 
 7  2 ¼
 14

Combine the like terms:

CHAPTER 12 Monomials and Polynomials 241