Factor the expression $9xy^2 + 6x^2y^2 + 21y^3$.

1. Problem Description

Factor the expression $9xy^2 + 6x^2y^2 + 21y^3$.

2. Solution Steps

First, find the greatest common factor (GCF) of the coefficients: 9, 6, and

2

1. The GCF is

3. Next, find the common variables with the lowest exponent:

The variables present are $x$ and $y$. The first term has $x$ and $y^2$, the second term has $x^2$ and $y^2$, and the third term has $y^3$. Therefore the only common variable is $y$.

The lowest power of $y$ in these three terms is $y^2$.

So, the GCF of the three terms is $3y^2$.

Now, factor out the GCF from the expression:

$9xy^2 + 6x^2y^2 + 21y^3 = 3y^2(3x) + 3y^2(2x^2) + 3y^2(7y)$

Factoring out $3y^2$ from each term, we get:

$3y^2(3x + 2x^2 + 7y)$

3. Final Answer

The factored expression is $3y^2(3x + 2x^2 + 7y)$.