Answer
The factor of the polynomial $8{{x}^{6}}-64{{y}^{6}}$ is$8\left( {{x}^{2}}-2{{y}^{2}} \right)\left( {{x}^{4}}+2{{x}^{2}}{{y}^{2}}+4{{y}^{4}} \right)$.
Work Step by Step
$8{{x}^{6}}-64{{y}^{6}}$
The factor of the polynomial $8{{x}^{6}}-64{{y}^{6}}$ is calculated as follows.
$\begin{align}
& 8{{x}^{6}}-64{{y}^{6}}=8\cdot {{x}^{6}}-8\cdot 8{{y}^{6}} \\
& =8\left( {{x}^{6}}-8{{y}^{6}} \right)\text{ } \\
& =8\left( {{\left( {{x}^{2}} \right)}^{3}}-{{\left( 2{{y}^{2}} \right)}^{3}} \right)\text{ }
\end{align}$
Use the formula${{A}^{3}}-{{B}^{3}}=\left( A-B \right)\left( {{A}^{2}}+A\cdot B+{{B}^{2}} \right)$ to solve the above expression as,
$\begin{align}
& 8{{x}^{6}}-64{{y}^{6}}=8\left( {{x}^{2}}-2{{y}^{2}} \right)\left( {{\left( {{x}^{2}} \right)}^{2}}+2{{x}^{2}}{{y}^{2}}+{{\left( 2{{y}^{2}} \right)}^{2}} \right) \\
& =8\left( {{x}^{2}}-2{{y}^{2}} \right)\left( {{x}^{4}}+2{{x}^{2}}{{y}^{2}}+4{{y}^{4}} \right)
\end{align}$
