Easy Algebra Step-by-Step

120 Easy Algebra Step-by-Step

2. (xy)^2 =x^2 y^2 , but (x+y)^2 ≠x^2 +y^2.


3. |xy| = |x| |y|, but |x−y| ≠ |x| − |y|.

4.

xy

x

=y, but

xy

x

y

+

≠+ (^1) ; also,
xy
x
xyx
xx
y

• ≠


• 
  

  ≠.

  
  

5.^111
xy xy

=⋅, but^111

xy+ xy

≠+.

6. 221 22
   xy^2
   − 2 =xy^2 , but 221 22
   xy^2
   − 2 ≠xyx^22.

a. From the statements of equality and inequality in sentences 1–6, list those

involving terms.

b. From the statements of equality and inequality in sentences 1–6, list those

involving factors and no terms.

Solution

a. From the statements of equality and inequality in sentences 1–6, list those

involving terms.

Step 1. Examine sentences 1–6 for equality or inequality statements involv-

ing terms and then list those involving terms.

xy+≠y xy+ , ()xy+ ≠+xxy

(^222)

• , xy−≠y xy,
  xy
  x
  y

+

≠1,+y

111

xy+ x y

≠+,

1

22

22

xy

− 2 xy

+

≠+x^2 (Note that the statements involv-

ing terms contain the ≠ symbol.)

b. From the statements of equality and inequality in sentences 1–6, list those

involving factors and no terms.

Step 1. Examine sentences 1–6 for equality or inequality statements involv-

ing terms and then list those not involving terms.

xy= xyx , (xy)^2 = x^2 y^2 , |xy| = |x||y|,

xy

x

=y,

111

xy xy

=⋅,

1

22

22

xy

− 2 =xy (Note that the statements involving factors and no

terms contain the = symbol.)

Greatest Common Factor

The previous problem should motivate you to become profi cient in factoring

polynomials. The discussion begins with factoring out the greatest common