# The blank in the statement “The Special Product Formula for the “square of a sum” is ( A + B ) 2 = _ . So ( 2 x + 3 ) 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 3E
To determine

## To fill: The blank in the statement “The Special Product Formula for the “square of a sum” is (A+B)2=                   _. So (2x+3)2=                   _”.

Expert Solution

The complete statement is “The special product formula for “square of a sum” is (A+B)2=A2+2AB+B2_. So (2x+3)2=(4x2+12x+9)_”.

### Explanation of Solution

Formula used:

If A and B are two real numbers then the special product formula for the “square of a sum” is, (A+B)2=A2+2AB+B2.

Calculation:

The given expression is (2x+3)2 which of the form (A+B)2 where A=2x,B=3.

Substitute A=2x,B=3 in (A+B)2=A2+2AB+B2 as follows:

(2x+3)2=(2x)2+2(2x)(3)+(3)2=4x2+12x+9

Therefore, the special product formula for “square of a sum” is (A+B)2=A2+2AB+B2_. So (2x+3)2=(4x2+12x+9)_.

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