Question

completely factor the expression $-\frac{4}{5}gn^{5}-\frac{5}{6}g^{5}n^{7}$.
$-\frac{4}{5}gn^{5}-\frac{5}{6}g^{5}n^{7}=square$ (simplify your answer. factor completely.)

Explanation:

Step1: Find the GCF of the coefficients

The coefficients are $-\frac{4}{5}$ and $-\frac{5}{6}$. The least - common multiple of 5 and 6 is 30. The GCF of the absolute - values of the coefficients in terms of non - fraction form after getting a common denominator is 1. For the variables, the common factors of $gn^{5}$ and $g^{5}n^{7}$ are $gn^{5}$.

Step2: Factor out the GCF

\[

$$\begin{align*} -\frac{4}{5}gn^{5}-\frac{5}{6}g^{5}n^{7}&=-\frac{1}{30}gn^{5}(24 + 25g^{4}n^{2}) \end{align*}$$

\]

Answer:

$-\frac{1}{30}gn^{5}(24 + 25g^{4}n^{2})$