Answer
$\color{blue}{(y-3)(y+3)(x-2)(x^2+2x+4)}$
Work Step by Step
Group the first two terms together and the last two terms together to obtain:
$=(x^3y^2-9x^3)+(-8y^2+72)$
Factor out $x^3$ in the first group and $-8$ in the second group to obtain:
$=x^3(y^2-9)+(-8)(y^2-9)$
Factor out the GCF $y^2-9$ to obtain:
$=(y^2-9)(x^3-8)
\\=(y^2-3^2)(x^3-2^3)$
Factor the difference of two squares using the formula $a^2-b^2=(a-b)(a+b)$ to obtain:
$=(y-3)(y+3)(x^3-2^3)$
Factor the difference of two cubes using the formula $a^3-b^3=(a-b)(a^2+ab+b^2)$ with $a=x$ and $b=2$ to obtain:
$=(y-3)(y+3)(x-2)(x^2+x(2)+2^2)
\\=\color{blue}{(y-3)(y+3)(x-2)(x^2+2x+4)}$
