Question

In the following exercises, factors completely:

$3x^2-75y^2$.

Short answer

The factors for the expression is,$3(x+5y)(x-5y)$.

Step-by-step solution

Step 1. Given Information.

The expression is,

$3x^2-75y^2$.

Step 2. Factor completely.

Taking $3$common out,

$3x^2-75y^2=3(x^2-25y^2)$

Using $a^2-b^2=(a+b)(a-b)$,

$3(x^2-25y^2)=3[{\left(x\right)}^2-{\left(5y\right)}^2]$

$=3(x+5y)(x-5y)$.