Page 132 - MarceAlgebra Demystified

CHAPTER 6 Factoring 119

p ffiffiffi p ffiffiffi p ffiffiffi p ffiffiffi
4: 8 x x ¼ð8 1Þ x ¼ 7 x
2
2
2
2
2
2
2
2
5: 2xy 4x y 7xy þ 17x y ¼ 2xy 7xy 4x y þ 17x y
2 2
¼ð2 7Þxy þð 4 þ 17Þx y
2
2
¼ 5xy þ 13x y
6: 14x þ 8 ð2x 4Þ¼ 14x þ 8 2x þ 4 ¼ 14x 2x þ 8 þ 4
¼ð14 2Þx þ 12 ¼ 12x þ 12
4 2 4 2
7: 16x þ 3x 4x þ 9x x þ 5x 6
¼ 16x 4 þ 9x 4 þ 3x 2 x 2 4x þ 5x 6
¼ð16 þ 9Þx 4 þð3 1Þx 2 þð 4 þ 5Þx 6
¼ 25x 4 þ 2x 2 þ x 6
p ffiffiffi p ffiffiffiffiffiffi p ffiffiffi p ffiffiffiffiffiffi
8: 5x y þ 7 xy þ 1 ð3x y 7 xy þ 4Þ
p p p p
¼ 5x y þ 7 xy þ 1 3x y þ 7 xy 4
ffiffiffi
ffiffiffi
ffiffiffiffiffiffi
ffiffiffiffiffiffi
p ffiffiffi p ffiffiffi p ffiffiffiffiffiffi p ffiffiffiffiffiffi
¼ 5x y 3x y þ 7 xy þ 7 xy þ 1 4
p p
¼ð5 3Þx y þð7 þ 7Þ xy 3
ffiffiffi
ffiffiffiffiffiffi
p ffiffiffi p ffiffiffiffiffiffi
¼ 2x y þ 14 xy 3
2 2 2 2
9: x y þ xy þ 6x þ 4 ð4x y þ 3xy 2x þ 5Þ
2
2
2
2
¼ x y þ xy þ 6x þ 4 4x y 3xy þ 2x 5
2
2
2
2
¼ x y 4x y þ xy 3xy þ 6x þ 2x þ 4 5
2
2
¼ð1 4Þx y þð1 3Þxy þð6 þ 2Þx 1
2
2
¼ 3x y 2xy þ 8x 1
Adding/Subtracting Fractions
With the distributive property and the ability to combine like terms, the
numerator of fraction sums/differences can be simplified. For now, we will
leave the denominators factored.