Factor:$15x^{3}y-3x^2{y}^2+6x{y}^3$

The given expression is$15x^{3}y-3x^2{y}^2+6x{y}^3$.

• Factor each of the terms in the given expression.

$$\begin{gathered} 15x^{3}y=3·5·x·x·x·y \\ 3x^2{y}^2=3·x·x·y·y \\ 6x{y}^3=2·3·x·y·y·y \end{gathered}$$

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

$3·x·y=3xy$

• So, the GCF of the terms of the given expression is $3xy$.

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

$3xy·5x^2-3xy·xy+3xy·2y^2$

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

role="math" localid="1644851304860" $3xy·5x^2-3xy·xy+3xy·2y^2=3xy(5x^2-xy+2y^2)$

• Multiply the obtained factors.

$\begin{array}{rcl}3xy(5x^2-xy+2y^2)& =& 3xy·5x^2-3xy·xy+3xy·2y^2\\ & =& 15x^{3}y-9x^2{y}^2+6x{y}^3\end{array}$

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