Answer
$16x^4-32x^3y^3+24x^2y^6-8xy^9+y^{12}$.
Work Step by Step
The given expression is
$=(2x-y^3)^4$
We have $a=2x$ and $b=-y^3$
Use the Binomial Theorem.
$(2x-y^3)^4$
$=[2x+(-y^3)]^4$
$=\binom{4}{0}(2x)^4+\binom{4}{1}(2x)^3(-y^3)+\binom{4}{2}(2x)^2(-y^3)^2+\binom{4}{3}(2x)^1(-y^3)^3+\binom{4}{4}(-y^3)^4$
Simplify.
$=\frac{4!}{0!4!}(2x)^4+\frac{4!}{1!3!}(2x)^3(-y^3)+\frac{4!}{2!2!}(2x)^2(-y^3)^2+\frac{4!}{3!1!}(2x)^1(-y^3)^3+\frac{4!}{4!0!}(-y^3)^4$
$=1(2x)^4+4(2x)^3(-y^3)+6(2x)^2(-y^3)^2+4(2x)^1(-y^3)^3+1(-y^3)^4$
$=16x^4-32x^3y^3+24x^2y^6-8xy^9+y^{12}$.
