Answer
$1024 a^5 + 1280 a^4 b + 640 a^3 b^2 + 160 a^2 b^3 + 20 a b^4 + b^5$
Work Step by Step
Using the Binomial Formula, the expression $
(4a+b)^5
$ expands to
\begin{array}{l}
(4a)^5b^0+
\dfrac{5}{1!}(4a)^4b^1+
\dfrac{5\cdot4}{2!}(4a)^3b^2+
\dfrac{5\cdot4\cdot3}{3!}(4a)^2b^3+\\
\dfrac{5\cdot4\cdot3\cdot2}{4!}(4a)^1b^4+
\dfrac{5\cdot4\cdot3\cdot2\cdot1}{5!}(4a)^0b^5
\\\\=
1024 a^5 + 1280 a^4 b + 640 a^3 b^2 + 160 a^2 b^3 + 20 a b^4 + b^5
\end{array}
