Pre-Algebra Demystified

2x
7x¼
5x

Hence,ðx
 7 Þðxþ 2 Þ¼x^2 
5x
14.

PRACTICE

Multiply:

1. (xþ6)(xþ7)


2. (x
   4)(x
   6)


3. (xþ9)(x
   11)


4. (x
   3)(xþ3)


5. (xþ4)(xþ4)

ANSWERS

1. x^2 þ13xþ 42


2. x^2
   10xþ 24


3. x^2
   2x
   99


4. x^2
   9


5. x^2 þ8xþ 16

Squaring a Binomial

Another special product results from squaring a binomial. This can be done

by using the two methods shown previously; however, a short-cut rule can be

used. It is:

ðaþbÞ^2 ¼a^2 þ2abþb^2

ða
bÞ^2 ¼a^2 
2abþb^2

In words, whenever you square a binomial, square the first term and then

multiply the product of the first and second terms by 2 and square the last

term.

EXAMPLE

Square (xþ8).

SOLUTION

ðxþ 8 Þ^2 ¼x^2 þ 2 x 8 þ 82

¼x^2 þ16xþ 64

242 CHAPTER 12 Monomials and Polynomials