# The blank in the statement “The Special Factoring Formula for the difference of squares is A 2 − B 2 = _ . So 4 x 2 − 25 factor as _ ”. ### 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 5E
To determine

## To fill: The blank in the statement “The Special Factoring Formula for the difference of squares is A2−B2=                   _. So 4x2−25 factor as                    _”.

Expert Solution

The complete statement is “The Special Factoring Formula for the difference of squares is A2B2=(A+B)(AB)_. So 4x225 factor as (2x+5)(2x5)_”.

### Explanation of Solution

Formula used:

If A and B are two real numbers then the special product formula for the “difference of squares” is A2B2=(A+B)(AB).

Calculation:

The given expression is 4x225 which of the form A2B2 where A2=4x2,B2=25.

Obtain the value of A as shown below.

A2=4x2A=2x

Similarly, obtain the value of B as follows.

B2=25B=5

Substitute A=2x and B=5 in A2B2=(A+B)(AB) as follows:

4x225=(2x+5)(2x5)

Therefore, the Special Factoring Formula for the difference of squares is A2B2=(A+B)(AB)_. So 4x225 factor as (2x+5)(2x5)_.

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