Algebra Demystified 2nd Ed

Chapter 6 FaCtoring and the distributive ProPerty 145

EXAMPLES

Completely factor the expression.

2 x(3x + y) + 5 y(3x + y)

We can factor 3x + y from each term, leaving 2x and 5y inside the parentheses.

2 x(3x + y) + 5 y(3x + y) = ( 2 x + 5 y)(3x + y)

10 y(x – y) + x – y = 10 y(x – y) + 1 (x – y) = ( 10 y + 1 )(x – y)

8 (2x – 1) + 2 x(2x – 1) – 3 y(2x – 1) = ( 8 + 2 x – 3 y)(2x – 1)

PRACTICE

Completely factor the expression.

1. 2(x − y) + 3y(x − y) =


2. 4(2 + 7x) − x(2 + 7x) =


3. 3(3 + x) + x(3 + x) =


4. 6x(4 − 3x) − 2y(4 − 3x) − 5(4 − 3x) =


5. 2x + 1 + 9x(2x + 1) =


6. 3(x − 2y)^4 + 2x(x − 2y)^4 =

✔SOLUTIONS

1. 2(x − y) + 3y(x − y) = (2 + 3y)(x − y)


2. 4(2 + 7x) − x(2 + 7x) = (4 − x)(2 + 7x)


3. 3(3 + x) + x(3 + x) = (3 + x)(3 + x) = (3 + x)^2


4. 6x(4 − 3x) − 2y(4 − 3x) − 5(4 − 3x) = (6x − 2y − 5)(4 − 3x)


5. 2x + 1 + 9x(2x + 1) = 1(2x + 1) + 9x(2x + 1) = (1 + 9x)(2x + 1)


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

More Factoring

An algebraic expression raised to different powers might appear in different

terms. The common factor is the expression raised to the lowest power.

EXAMPLES

Completely factor the expression.

PRACTICE

Completely factor the expression.