Answer
$(xy+1)(x^2y^2-xy+1)(x-2)(x^2+2x+4)$.
Work Step by Step
The given expression is
$=x^6y^3+x^3-8x^3y^3-8$
Group the terms.
$=(x^6y^3+x^3)+(-8x^3y^3-8)$
Factor each term.
$=x^3(x^3y^3+1)-8(x^3y^3+1)$
Factor out $(x^3y^3+1)$
$=(x^3y^3+1)(x^3-8)$
We can write.
$=(x^3y^3+1^3)(x^3-2^3)$
Use algebraic identities.
$(a^3-b^3)=(a-b)(a^2+ab+b^2)$
and $(a^3+b^3)=(a+b)(a^2-ab+b^2)$
$=(xy+1)(x^2y^2-xy+1)(x-2)(x^2+2x+4)$.
