# The blank in the statement “The special product formula for “product of the sum and difference of terms” is ( A + B ) ( A − B ) = _ _ _ _ _ _ . So ( 5 + x ) ( 5 − x ) = _ _ _ _ _ ”. ### 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 4E
To determine

## To fill: The blank in the statement “The special product formula for “product of the sum and difference of terms” is (A+B)(A−B)=______. So (5+x)(5−x)=_____”.

Expert Solution

The complete statement is “The special product formula for “product of the sum and difference of terms” is (A+B)(AB)=A2B2_. So (5+x)(5x)=(25x2)_”.

### Explanation of Solution

Formula used:

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

Calculation:

The given expression is (5+x)(5x) which of the form (A+B)(AB) where A=5,B=x.

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

(5+x)(5x)=(5)2(x)2=25x2

Therefore, the complete statement is “The special product formula for “product of the sum and difference of terms” is (A+B)(AB)=A2B2_. So (5+x)(5x)=(25x2)_”.

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