Factor:$8a^{3}b+2a^2{b}^2-6a{b}^3$.

The given information is$8a^{3}b+2a^2{b}^2-6a{b}^3$.

• Factor each of the terms in the given expression.

$$\begin{gathered} 8a^{3}b=2·2·2·a·a·a·b \\ 2a^2{b}^2=2·a·a·b·b \\ 6a{b}^3=2·3·a·b·b·b \end{gathered}$$

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

$2·a·b=2ab$

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

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

$2ab·4a^2+2ab·ab-2ab·3b^2$

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

role="math" localid="1644851780710" $2ab·4a^2+2ab·ab-2ab·3b^2=2ab(4a^2+ab-3b^2)$

• Multiply the obtained factors.

$\begin{array}{rcl}2ab(4a^2+ab-3b^2)& =& 2ab·4a^2+2ab·ab-2ab·3b^2\\ & =& 8a^{3}b+2a^2{b}^2-6a{b}^3\end{array}$

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