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