Chapter 10, Problem 1R

To determine

To calculate: The product of the expression $\left(c+d\right)\left(c-d\right)$ mentally.

Answer to Problem 1R

Solution:

The product of the expression $\left(c+d\right)\left(c-d\right)$ is $c^2-d^2$.

Explanation of Solution

Given Information:

The expression is $\left(c+d\right)\left(c-d\right)$.

Formula used:

Steps to calculate product mentally:

1) The product of the first terms of binomials gives the first term of the product.

2) The sum of the outer and inner product of binomials gives the middle term of the product.

3) The product of the last terms of the binomials gives the last term of the product.

Calculation:

Consider the provided expression $\left(c+d\right)\left(c-d\right)$.

$\begin{array}{c}\left(c+d\right)\left(c-d\right)=c^2-cd+cd-d^2\\ =c^2-d^2\end{array}$

Therefore, the product of the expression $\left(c+d\right)\left(c-d\right)$ is $c^2-d^2$.