Chapter 8.7, Problem 3P

a.

To determine

To write: The factored form of the given expression.

Explanation of Solution

Given information:

The given expression is $v^2-100$

Calculation:

Factorize $v^2-100$

  $\begin{array}{l}{v}^2-100\\ =v^2-10v+10v-100\\ =v(v-10)+10(v-10)\\ =(v-10)(v+10)\end{array}$

Hence, the factored form of given expression is $(v-10)(v+10)$

b.

To determine

To write: The factored form of the given expression.

Explanation of Solution

Given information:

The given expression is $s^2-16$

Calculation:

Factorize $s^2-16$

  $\begin{array}{l}{s}^2-16\\ =s^2-4v+4s-16\\ =s(s-4)+4(s-4)\\ =(s-4)(s+4)\end{array}$

Hence, the factored form of given expression is $(s-4)(s+4).$