Page 130 - MarceAlgebra Demystified

CHAPTER 6 Factoring 117

2: 50ð3 xÞ¼ 150 þ 50x

2 2
3: 12xyð 2x þ yÞ¼ 24x y 12xy
2
3
2
4: 7x ð x 4yÞ¼ 7x þ 28x y
2
5: 6yð 3x y þ 4Þ¼ 18xy þ 6y 24y

Combining Like Terms

Two or more terms are alike if they have the same variables and the
2
2
exponents (or roots) on those variables are the same: 3x y and 5x y are
2
like terms but 6xy and 4xy are not. Constants are terms with no variables.
2 3
The number in front of the variable(s) is the coefficient—in 4x y , 4 is the
coefficient. If no number appears in front of the variable, then the coeffi-
cient is 1. Add or subtract like terms by adding or subtracting their
coefficients.

Examples

2
2
2
2
3x y þ 5x y ¼ð3 þ 5Þx y ¼ 8x y
p ffiffiffi p ffiffiffi p ffiffiffi p ffiffiffi
14 x 10 x ¼ð14 10Þ x ¼ 4 x
8xyz þ 9xyz 6xyz ¼ð8 þ 9 6Þxyz ¼ 11xyz
3x þ x ¼ 3x þ 1x ¼ð3 þ 1Þx ¼ 4x

p p p p p p
7x y x y ¼ 7x y 1x y ¼ð7 1Þx y ¼ 6x y
ffiffiffi
ffiffiffi
ffiffiffi
ffiffiffi
ffiffiffi
ffiffiffi
2 2 3 2 5 2 3 2 5
x 4xy þ x þ xy ¼ þ x þ 4 þ xy
3 4 2 3 4 2

8 9 2 8 5 17 2 3
¼ þ x þ þ xy ¼ x xy
12 12 2 2 12 2