Answer
$a^5x^5+5a^4bx^4y+10a^3b^3x^3y^2+10a^2b^3x^2y^3+5ab^4xy^4+b^5y^5$
Work Step by Step
We are given the expression:
$(ax+by)^5$
Use the Binomial Theorem to expand the expression:
$(ax+by)^5=\sum_{k=0}^5 \binom{5}{k}(ax)^{5-k}(by)^k$
$=\binom{5}{0}(ax)^5(by)^0+\binom{5}{1}(ax)^4(by)^1+\binom{5}{2}(ax)^3(by)^2+\binom{5}{3}(ax)^2(by)^3+\binom{5}{4}(ax)^1(by)^4+\binom{5}{5}(ax)^0(by)^5$
$=a^5x^5+5a^4bx^4y+10a^3b^2x^3y^2+10a^2b^3x^2y^3+5ab^4xy^4+b^5y^5$
