Question

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

Short answer

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

Step-by-step solution

Step 1. Given Information

The given expression is$9x{y}^2+6x^2{y}^2+21y^3$.

Step 2. Find GCF of the terms

• Factor each of the terms in the given expression.

$$\begin{gathered} 9x{y}^2=3·3·x·y·y \\ 6x^2{y}^2=3·2·x·x·y·y \\ 21y^3=3·7·y·y·y \end{gathered}$$

• From the obtained factors, it is observed that the common factors are $3,y,y$.
• Multiply the common factors to determine the GCF of the terms of given expression.

$3·y·y=3y^2$

• So, the GCF of the terms of the given expression is $3y^2$.

Step 3. Rewrite the given expression

• Express each of the term of the given expression as a product of GCF, $3y^2$.

$9x{y}^2+6x^2{y}^2+21y^3=3y^2·3x+3y^2·2x^2+3y^2·7y$

• Use the reverse distributive property, $ab+ac=a(b+c)$to rewrite the obtained expression.

role="math" localid="1644474114040" $3y^2(3x+2x^2+7y)$

Step 4. Check

• Multiply the factors obtained.

$\begin{array}{rcl}3y^2(3x+2x^2+7y)& =& 3y^2·3x+3y^2·2x^2+3y^2·7y\\ & =& 9y^{2}x+6x^2{y}^2+3y^{2}7y\end{array}$

• Since the obtained expression is the same as the given expression, the obtained factors are verified.