Page 128 - MarceAlgebra Demystified

CHAPTER 6 Factoring 115

Sometimes you will need to ‘‘distribute’’ a minus sign or negative sign:
ða þ bÞ¼ a b and ða bÞ¼ a þ b. You can use the distributive
properties and think of ða þ bÞ as ð 1Þða þ bÞ and ða bÞ as
ð 1Þða bÞ:
ða þ bÞ¼ð 1Þða þ bÞ¼ð 1Þa þð 1Þb ¼ a þ b ¼ a b

and
ða bÞ¼ð 1Þða bÞ¼ð 1Þa ð 1Þb ¼ a ð 1Þb
¼ a ð bÞ¼ a þ b:
A common mistake is to write ða þ bÞ¼ a þ b and ða bÞ¼ a b.
The minus sign and negative sign in front of the parentheses changes the signs
of every term (a quantity separated by a plus or minus sign) inside the
parentheses.

Examples

2
ð3 þ xÞ¼ 3 x ðy x Þ¼ y þ x 2
ð 2 þ yÞ¼ 2 y ð 9 yÞ¼ 9 þ y

2
2
ð2 þ x 3yÞ¼ 2 x þ 3y ðx x 2Þ¼ x þ x þ 2
ð 4x 7y 2Þ¼ 4x þ 7y þ 2

Practice

1: ð4 þ xÞ¼

2: ð x yÞ¼
2
3: ð2x 5Þ¼
2
4: ð 18 þ xy Þ¼

5: ð2x 16y þ 5Þ¼
2
6: ðx 5x 6Þ¼