Question

Factor:$9x{y}^2+6x^2{y}^2+21y^3$

Short answer

The required factor is$3y^2\left(3x+2x^2+7y\right)$.

Step-by-step solution

Step 1. Given information.

The given polynomial is:

$9x{y}^2+6x^2{y}^2+21y^3$

Step 2. Find the GCF.

Find the GCF of $9x{y}^2,6x^2{y}^2,\mathrm{and}21y^3$,

role="math" localid="1647710482910" $$\begin{gathered} 9x{y}^2=3·3·x·y·y \\ 6x^2{y}^2=2·3·x·x·y·y \\ 21y^3=3·7·y·y·y \end{gathered}$$

GCF is:

role="math" localid="1647710505787" $$\begin{gathered} =3·y·y \\ =3y^2 \end{gathered}$$

Step 3. Find the factor.

Rewrite each term as a product using the GCF,

$3y^2·3x+3y·2x^2+3y·7y$

Factor the GCF,

$3y^2\left(3x+2x^2+7y\right)$