Question

Factor the Greatest Common Factor from a Polynomial.

$12x{y}^2+18x^2{y}^2-30y^3$

Short answer

The required answer is$6y^2\left(2x+3x^2-5y\right)$.

Step-by-step solution

Step 1. Given information.

The given binomial is$12x{y}^2+18x^2{y}^2-30y^3$.

Step 2.  Simplify the expression. 

Apply exponent rule.

$$\begin{gathered} 12x{y}^2+18x^2{y}^2-30y^3 \\ =12x{y}^2+18x^2{y}^2-30y^{2}y \\ =2·\hspace{0.17em}6x{y}^2+3·\hspace{0.17em}6x^2{y}^2+5·\hspace{0.17em}6y^{2}y \end{gathered}$$

Factor out common term.

$6y^2\left(2x+3x^2-5y\right)$