Answer
$a^4x^4-4a^3bx^3y+6a^2b^2x^2y^2-4ab^3xy^3+b^4y^4$
Work Step by Step
We are given the expression:
$(ax-by)^4$
Use the Binomial Theorem to expand the expression:
$(ax-by)^4=\sum_{k=0}^4 \binom{4}{k}(ax)^{4-k}(-by)^k$
$=\binom{4}{0}(ax)^4(-by)^0+\binom{4}{1}(ax)^3(-by)^1+\binom{4}{2}(ax)^2(-by)^2+\binom{4}{3}(ax)^1(-by)^3+\binom{4}{4}(ax)^0(-by)^4$
$=a^4x^4+4a^3x^3(-by)+6a^2x^2(b^2y^2)+4ax(-b^3y^3)+b^4y^4$
$=a^4x^4-4a^3bx^3y+6a^2b^2x^2y^2-4ab^3xy^3+b^4y^4$
