Algebra Demystified 2nd Ed

146 algebra De mystif ieD

EXAMPLES

Completely factor the expression.

6(x + 1)^2 – 5(x + 1)

Each term has x + 1 as a factor. The smallest power on this factor is 1, so the

common factor is ()x+ 11.

6(x + 1)^2 – 5(x + 1) = [6(x + 1)](x + 1) – 5 (x + 1)

= [6(x + 1) – 5](x + 1) = (6x + 6 – 5)(x + 1) = (6x + 1)(x + 1)

10(2x – 3)^3 + 3(2x – 3)^2 = [10( 2 x – 3)](2x – 3)^2 + 3 (2x – 3)^2 = [10(2x – 3) + 3](2x – 3)^2

=(20x – 30 + 3)(2x – 3)^2 = (20x – 27)(2x – 3)^2

9(14x + 5)^4 + 6x(14x + 5) – (14x + 5) = [9(14x + 5)^3 ](14x + 5) + 6 x(14x + 5) – 1 (14x + 5)

= [9(14x + 5)^3 + 6x – 1](14x + 5)

PRACTICE

Completely factor the expression.

1. 8(x + 2)^3 + 5(x + 2)^2 =


2. −4(x + 16)^4 + 9(x + 16)^2 + x + 16 =


3. (x + 2y)^3 − 4(x + 2y) =


4. 2(x^2 − 6)^9 + (x^2 − 6)^4 + 4(x^2 − 6)^3 + (x^2 − 6)^2 =


5. (15xy − 1)(2x − 1)^3 − 8(2x − 1)^2 =

✔SOLUTIONS

1. 8(x + 2)^3 + 5(x + 2)^2 = [ 8 (x + 2 )](x + 2)^2 + 5 (x + 2)^2
   = [ 8 (x + 2 ) + 5 ](x + 2)^2
   = (8x + 16 + 5)(x + 2)^2 = (8x + 21)(x + 2)^2


2. −4(x + 16)^4 + 9(x + 16)^2 + x + 16
   = [− 4 (x + 16 )^3 ](x + 16) + 9 (x + 16 )(x + 16) + 1 (x + 16)
   = [−4(x + 16 )^3 + 9 (x + 16 ) + 1 ](x + 16)
   = [−4(x + 16)^3 + 9x + 144 + 1](x + 16)
   = [−4(x + 16)^3 + 9x + 145)(x + 16)


3. (x + 2y)^3 − 4(x + 2y) = (x + 2 y)^2 (x + 2y) − 4 (x + 2y)
   = [(x + 2 y)^2 − 4 ](x + 2y)

EXAMPLES

Completely factor the expression.

PRACTICE

Completely factor the expression.