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# Factor out the common factor

Factor out the common factor.
(5x - 2)2 + (5x - 2)

Completely factor the expression.
x4 - 3x3 + x2 - 3x
Write the rational expression in simplest form.
4x2y
xy - y

Write the rational expression in simplest form.
9x2 + 9x
8x + 8

Write the rational expression in simplest form.
x2 - 9
3 - x

Perform the multiplication and simplify.
x + 4
x3(9 - x)
· x(x - 9)
13

Perform the division and simplify.
3y - 12
8y + 24
÷ 4 - y
5y + 15

Factor the expression by removing the common factor with the smaller exponent. (Factor your answer completely.)
x5 - 3x-4

Factor the expression by removing the common factor with the smaller exponent. (Factor your answer completely.)
4x(x - 8)-6 - 12x2(x - 8)-7

Divide and simplify. See Examples 6-8.
x2 + 16
3(x + 7)
÷ x + 4
3(x2 - 49)

, x ≠ ±7

Insert the required factor in the parentheses.
3x6
4
= 3
4

( )

Insert the required factor in the parentheses.
5
7
x + 1
2
= 1
7

( )

Insert the required factor in the parentheses.
3(6x + 1)x1/2 + 4x3/2
STEP 1: Factor out x1/2.
x1/2(3( ) + )

STEP 2: Combine like terms.
x1/2(_ )

Write the following expression using negative exponents.
x + 5
x(2-x)1/3

Write the fraction as a sum of two or more terms.
x10 - 5x7 + 6
x2

Simplify the expression.
x5(-2)(x2 + 3)-4(2x) - (x2 + 3)-3(2)x4
(x5)2

Simplify the expression.
(4x - 1)1/2 - (x + 2)(4x - 1)-1/2

#### Solution Preview

Factor out the common factor.
(5x - 2)2 + (5x - 2)

Completely factor the expression.
x4 - 3x3 + x2 - 3x

Write the rational expression in simplest form.
4x2y
xy - y

Write the rational expression in simplest form.
9x2 + 9x
8x + 8

Write the rational expression in simplest form.
x2 - 9
3 - x

Perform the multiplication and simplify.
x + 4 ...

#### Solution Summary

The expert factors out the common factor.

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