Question

completely factor $24a^{4}d^{2}-30a^{3}d^{4}+18a^{6}d$.
$24a^{4}d^{2}-30a^{3}d^{4}+18a^{6}d=square$ (simplify your answer. factor completely.)

Explanation:

Step1: Find GCF of coefficients

The GCF of 24, - 30, and 18 is 6.

Step2: Find GCF of variables

For the variable \(a\), the lowest - power of \(a\) among \(a^{4},a^{3},a^{6}\) is \(a^{3}\). For the variable \(d\), the lowest - power of \(d\) among \(d^{2},d^{4},d\) is \(d\). So the GCF of the terms is \(6a^{3}d\).

Step3: Factor out the GCF

\[

$$\begin{align*} 24a^{4}d^{2}-30a^{3}d^{4}+18a^{6}d&=6a^{3}d(4ad - 5d^{3}+3a^{3}) \end{align*}$$

\]

Answer:

\(6a^{3}d(4ad - 5d^{3}+3a^{3})\)