# How do you factor 12x^3y^2 - 18xy^4?

Aug 7, 2016

$6 x {y}^{2} \left(2 {x}^{2} - 3 {y}^{2}\right)$

#### Explanation:

By finding $\textcolor{b l u e}{\text{common factors}}$ of the 2 terms of the expression.

• 12 and 18 have a $\textcolor{b l u e}{\text{common factor}}$ of 6

${x}^{3} \text{ and " x " have a " color(blue)("common factor") " of } x$

${y}^{2} \text{ and " y^4" have a " color(blue)("common factor")" of } {y}^{2}$

Hence the 'combined' color(blue)("common factor") " is " 6xy^2

$\Rightarrow 12 {x}^{3} {y}^{2} - 18 x {y}^{4} = 6 x {y}^{2} \left(2 {x}^{2} - 3 {y}^{2}\right)$