# The factor of the expression ( a 2 − 1 ) b 2 − 4 ( a 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 112E
To determine

## To calculate: The factor of the expression (a2−1)b2−4(a2−1) .

Expert Solution

The factor of the expression (a21)b24(a21) is (a1)(a+1)(b2)(b+2) .

### Explanation of Solution

Given information:

The expression (a21)b24(a21) .

Formula used:

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

A2B2=(A+B)(AB)

Calculation:

Consider the given expression (a21)b24(a21) .

Rewrite the expression as,

(a21)b24(a21)=(a21)(b24)

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

A2B2=(A+B)(AB)

Apply it,

(a21)b24(a21)=(a21)(b24)=[(a)2(1)2][(b)2(2)2]=(a1)(a+1)(b2)(b+2)

Thus, the factor of expression (a21)b24(a21) is (a1)(a+1)(b2)(b+2) .

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