# The blank in the statement “The Special Factoring Formula for perfect square is A 2 + 2 A B + B 2 = _ . So x 2 + 10 x + 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 6E
To determine

## To fill: The blank in the statement “The Special Factoring Formula for perfect square is A2+2AB+B2=                   _. So x2+10x+25 factor as                    _”.

Expert Solution

The complete statement is “The Special Factoring Formula for perfect square is A2+2AB+B2=(A+B)2_. So x2+10x+25 factor as (x+5)2_”.

### Explanation of Solution

The special factoring formula for perfect square is given by the formula A2+2AB+B2=(A+B)2.

Rewrite the given trinomial x2+10x+25 as x2+52x+52.

Note that x2+52x+52 is of the form A2+2AB+B2 where the middle is as follows:

2AB=2x5

Thus, A=x and B=5.

Substitute A=x and B=5 in A2+2AB+B2=(A+B)2 as follows:

x2+10x+25=(x+5)2

Therefore, the Special Factoring Formula for perfect square is A2+2AB+B2=(A+B)2_. So x2+10x+25 factor as (x+5)2_.

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