# How do you factor 3xy^2 - 12x?

Mar 7, 2018

See a solution process below:

#### Explanation:

First, we can find the Greatest Common Factor of each term:

$3 x {y}^{2} = 3 \times x \times {y}^{2}$

$3 x {y}^{2} = 3 \times 4 \times x$

The common factors are:

$3 x {y}^{2} = \textcolor{red}{3} \times \textcolor{red}{x} \times {y}^{2}$

$3 x {y}^{2} = \textcolor{red}{3} \times 4 \times \textcolor{red}{x}$

For a GCF of:

$G C F = \textcolor{red}{3} \times \textcolor{red}{x} = 3 x$

We can rewrite the express and then factor it as:

$\left(3 x \cdot {y}^{2}\right) - \left(3 x \cdot 4\right) \implies 3 x \left({y}^{2} - 4\right)$

Mar 7, 2018

$3 x \left(y - 2\right) \left(y + 2\right)$

#### Explanation:

We are given: $3 x {y}^{2} - 12 x$.

First, take out the greatest common factor of both numbers, that is $3 x$.

So, we get

$3 x \left({y}^{2} - 4\right)$

$= 3 x \left({y}^{2} - {2}^{2}\right)$

Know that, ${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$.

We can now let $a = y , b = 2$, and so the expression becomes

$= 3 x \left(y - 2\right) \left(y + 2\right)$

From here, we cannot simplify this further, and therefore this is the final answer.