Factor:$6y^3-15y^2$

The given expression is$6y^3-15y^2$.

• Factor each of the terms in the given expression.

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

• 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 the given expression.

$3·y·y=3y^2$

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

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

$3y^2·2y-3y^2·5$

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

role="math" localid="1644850753828" $3y^2·2y-3y^2·5=3y^2(2y-5)$

• Multiply the obtained factors.

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

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