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### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

# The Special Product Formula for the “product of the sum and difference of terms” is $\left(A+B\right)\left(A-B\right)=_____$. So, $\left(5+x\right)\left(5-x\right)=_____$

The Special Product Formula for the “product of the sum and difference of terms” is $\left(A+B\right)\left(A-B\right)={A}^{2}-{B}^{2}$. So, $\left(5+x\right)\left(5-x\right)=25-{x}^{2}$

See the step by step solution

## Step 1. Apply the special product formula of “product of the sum and difference of terms”.

If A and B are any real numbers or algebraic expressions, then

$\left(A+B\right)\left(A-B\right)={A}^{2}-{B}^{2}$

## Step 2. Analyze the given expression.

Given $\left(5+x\right)\left(5-x\right)$

Here width="82" style="max-width: none; vertical-align: -4px;" $A=5,B=x$

## Step 3. Solve the expression.

Substitute the values in the product of the sum and difference of terms formula to get:

$\begin{array}{l}\left(5+x\right)\left(5-x\right)={5}^{2}-{x}^{2}\\ ⇒\left(5+x\right)\left(5-x\right)=25-{x}^{2}\end{array}$