Chapter 8.7, Problem 33P

Factor each expression.

$8d^2-8$

To determine

To factor the expression $8d^2-8$

Answer to Problem 33P

The factors of the given expression are $8\left(d+1\right)\left(d-1\right)$ .

Explanation of Solution

Given information:

Given expression $8d^2-8$

  $\begin{array}{l}\text{Given}8d^2-8=8\left(d^2-1\right)\\ =8\left({\left(d\right)}^2-1^2\right)\end{array}$

As we know that $a^2-b^2=\left(a+b\right)\left(a-b\right)$

Put $a=d,b=1$ , we get ${\left(d\right)}^2-1^2=\left(d+1\right)\left(d-1\right)$

Multiplying $8$ on both sides, we get

  $8\left({\left(d\right)}^2-1^2\right)=8\left(d+1\right)\left(d-1\right)$

Hence, the factors of the given expression are $8\left(d+1\right)\left(d-1\right)$ .