# The factor of the expression x 2 ( x 2 − 1 ) − 9 ( x 2 − 1 ) .

### 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 111E
To determine

## To calculate: The factor of the expression x2(x2−1)−9(x2−1) .

Expert Solution

The factor of the expression x2(x21)9(x21) is (x1)(x+1)(x3)(x+3) .

### Explanation of Solution

Given information:

The expression x2(x21)9(x21) .

Formula used:

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

A2B2=(A+B)(AB)

Calculation:

Consider the given expression x2(x21)9(x21) .

Rewrite the expression as,

x2(x21)9(x21)=(x21)(x29)

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

A2B2=(A+B)(AB)

Apply it,

x2(x21)9(x21)=(x21)(x29)=[(x)2(1)2][(x)2(3)2]=(x1)(x+1)(x3)(x+3)

Thus, the factor of expression x2(x21)9(x21) is (x1)(x+1)(x3)(x+3) .

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