Answer
$1024 a^5 - 6400 a^4 b + 16000 a^3 b^2 - 20000 a^2 b^3 + 12500 a b^4 - 3125 b^5$
Work Step by Step
$(x+y)^n=\binom{n}{0}x^ny^0+\binom{n}{1}x^{n-1}y^1+...+\binom{n}{a}x^{n-a}y^a+..\binom{n}{n}x^{0}y^n$
Here: $n=4$, $x=4a$, $y=-5b$
$(4a-5b)^5=\binom{5}{0}(4a)^{5}(-5b)^0+\binom{5}{1}(4a)^{5-1}(-5b)^1+\binom{5}{2}(4a)^{5-2}(-5b)^2+\binom{5}{3}(4a)^{5-3}(-5b)^3+\binom{5}{4}(4a)^{5-4}(-5b)^4+\binom{5}{5}(4a)^{5-5}(-5b)^5=$
$1024 a^5 - 6400 a^4 b + 16000 a^3 b^2 - 20000 a^2 b^3 + 12500 a b^4 - 3125 b^5$
