Question

Factor completely, then place the answer in the proper location on the grid.

Answer 1

$\mathrm{Factor\:out\:common\:term\:}9 \ \textgreater \ 9\left(x^4-25y^8\right)$

$Factor \ \textgreater \ x^4-25y^8$

$\mathrm{Apply\:difference\:of\:squares\:rule:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)$
$x^2-5y^4=\left(x+\sqrt{5}y^2\right)\left(x-\sqrt{5}y^2\right)$

$x^2-5y^4 \ \textgreater \ \mathrm{Apply\:difference\:of\:squares\:rule:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)$
$x^2-5y^4=\left(x+\sqrt{5}y^2\right)\left(x-\sqrt{5}y^2\right)$

$\left(x^2+5y^4\right)\left(x+\sqrt{5}y^2\right)\left(x-\sqrt{5}y^2\right)$

$9\left(x^2+5y^4\right)\left(x+\sqrt{5}y^2\right)\left(x-\sqrt{5}y^2\right)$

Hope this helps!