Algebra Demystified 2nd Ed

Chapter 6 FaCtoring and the distributive ProPerty 175

6. 1 23
   4

1

1

23

4

1

1

4

4

23

4

− −^42

+

=− −

+

=⋅+

+

− −

+

x = +− −

x

x

x

x

x

x

x

xx( 33

4

42 3

4

7

4

)

x

xx

x

x

x

+

= +− +

+

=−+

+

7.^1
3

1

23

1

3

1

xx−^2 xxxx 31

+

−−

=

−

+

()−+()

=

−

⋅ +

+

+

−+

1

3

1

1

1

x 31

x

xx()()x

= ++

−+

= +

−

x

xx

x

x

11

31

2

()()() 3 (xx+1)

Summary

In this chapter, we learned how to:

•   Use the distributive property of multiplication over addition to rewrite expres-

sions. The distributive property is ab()±=±cabac. We generally use this

property where one or more of a, b, and c are variables.

•   Combine like terms. Terms are alike if they have the same variables raised

to the same powers. Combine like terms by adding their coefficients.

•   Distribute negative numbers and other negative symbols. Distributing a neg-

ative number, negative sign, or minus sign changes the sign of every term

inside the parentheses.

•   Perform basic factoring. Begin by writing each term as a product of numbers

and variables, dividing out the common factor(s) from each term. The

common factor goes outside of the parentheses, the terms go inside the

parentheses.

•   Factor by grouping. Some expressions having four terms can be factored

with a technique called factoring by grouping. Factor the first two terms

and look at the last pair of terms. If the last pair of terms can be factored

so that it has a common factor with the first pair of terms, factor out that

common factor. You are then left with two terms having a common factor.

Finish by factoring this common factor.