91Ó°ÊÓ

The given expression is$2x^3+12x^2$

• Factor each of the terms in the given expression.

$$\begin{gathered} 2x^3=2·x·x·x \\ 12x^2=2·2·3·x·x \end{gathered}$$

• From the obtained factors, it is observed that the common factors are $2,x,x$.
• Multiply the common factors to determine the GCF of the terms of the given expression.

$2·x·x=2x^2$

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

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

$2x^2·x+2x^2·6$

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

role="math" localid="1644850183257" $2x^2·x+2x^2·6=2x^2(x+6)$

• Multiply the obtained factors.

$\begin{array}{rcl}2x^2(x+6)& =& 2x^2·x+2x^2·6\\ & =& 2x^3+12x^2\end{array}$

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