# The factor of the expression x 5 2 − x 1 2 . ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.3, Problem 89E
To determine

## To calculate: The factor of the expression x52−x12 .

Expert Solution

The factor of the expression x52x12 is x(x+1)(x1) .

### Explanation of Solution

Given information:

The expression x52x12 .

Formula used:

To factor an expression, split the terms in the expression into multiplication of simpler expressions, then take the common power out and group the expressions together.

The special factoring formula for difference of squares, which is mathematically expressed as,

A2B2=(A+B)(AB)

Calculation:

Consider the given expression x52x12 .

Recall that to factor an expression, split the terms in the expression into multiplication of simpler expressions, then take the common power out and group the expressions together.

Apply it,

x52x12=x12(x52x121)=x12(x21)=x(x21)

Recall the special factoring formula for difference of squares, which is mathematically expressed as,

A2B2=(A+B)(AB)

Here, A=x2 and B=1 , so, apply the special factoring formula,

x52x12=x(x21)=x(x+1)(x1)

Thus, the factor of expression x52x12 is x(x+1)(x1) .

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