Page 126 - MarceAlgebra Demystified

CHAPTER 6

Factoring

Distributing Multiplication over Addition and

Subtraction

Distributing multiplication over addition (and subtraction) and factoring
(the opposite of distributing) are extremely important in algebra. The dis-
tributive law of multiplication over addition, aðb þ cÞ¼ ab þ ac, says that
you can first take the sum ðb þ cÞ then the product (a times the sum of b
and c) or the individual products ðab and ac) then the sum (the sum of ab and
ac). For instance, 12ð6 þ 4Þ could be computed as 12ð6 þ 4Þ¼ 12ð6Þþ 12ð4Þ
¼ 72 þ 48 ¼ 120 or as 12ð6 þ 4Þ¼ 12ð10Þ¼ 120. The distributive law of
multiplication over subtraction, aðb cÞ¼ ab ac, says the same about a
product and difference.

Examples

7ðx yÞ¼ 7x 7y 4ð3x þ 1Þ¼ 12x þ 4

2
3
3
2
4
x ð3x 5yÞ¼ 3x 5x y 8xyðx þ 4yÞ¼ 8x y þ 32xy 2
3 3
2
2
2 3
2 5
ffiffiffi
6x y ð5x 2y Þ¼ 30x y 12x y p xðx þ 12Þ¼ x 2 p ffiffiffi p ffiffiffi
x þ 12 x
4
2
2
2 4
y ð y þ 6Þ¼ y y þ 6y 2 ¼ y þ 6y 2
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