Question

In the following exercises, factor completely.
$4p^2-100$

Short answer

The factored form of the given expression is $4(p-5)(p+5)$.

Step-by-step solution

Step 1. Given information.

The given expression is:
$4p^2-100$

Step 2. Determine the factored form.

The given expression can be written as:
$\begin{array}{rcl}4p^2-100& =& 4(p^2-25)\\ & =& 4(p^2-5^2)\\ & =& 4(p-5)(p+5)[\because a^2-b^2=(a-b\left)\right(a+b\left)\right]\end{array}$

Step 3. Conclusion.

The factored form of the given expression is $4(p-5)(p+5)$.