Answer
$a^5 + 10 a^4 b + 40 a^3 b^2 + 80 a^2 b^3 + 80 a b^4 + 32 b^5$
Work Step by Step
Using the Binomial Formula, the expression $
(a+2b)^5
$ expands to
\begin{array}{l}
a^5(2b)^0+
\dfrac{5}{1!}a^4(2b)^1+
\dfrac{5\cdot4}{2!}a^3(2b)^2+
\dfrac{5\cdot4\cdot3}{3!}a^2(2b)^3+\\
\dfrac{5\cdot4\cdot3\cdot2}{4!}a^1(2b)^4+
\dfrac{5\cdot4\cdot3\cdot2\cdot1}{5!}a^0(2b)^5+
\\\\=
a^5 + 10 a^4 b + 40 a^3 b^2 + 80 a^2 b^3 + 80 a b^4 + 32 b^5
\end{array}
