# The factor of the expression ( a + b ) 2 − ( a − b ) 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 109E
To determine

## To calculate: The factor of the expression (a+b)2−(a−b)2 .

Expert Solution

The factor of the expression (a+b)2(ab)2 is 4ab .

### Explanation of Solution

Given information:

The expression (a+b)2(ab)2 .

Formula used:

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

A2B2=(A+B)(AB)

Calculation:

Consider the given expression (a+b)2(ab)2 .

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

A2B2=(A+B)(AB)

Here, the values of A and B are A=a+b and B=ab .

(a+b)2(ab)2=((a+b)+(ab))((a+b)(ab))=(a+b+ab)(a+ba+b)=(2a)(2b)=4ab

Thus, the factor of expression (a+b)2(ab)2 is 4ab .

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