Answer
$a^7+7a^6b+21a^5b^2+35a^4b^3+35a^3b^4+21a^2b^5+7ab^6+b^7$
Work Step by Step
Using the Binomial Formula, the expression $
(a+b)^7
$ expands to
\begin{array}{l}
a^7b^0+
\dfrac{7}{1!}a^6b^1+
\dfrac{7\cdot6}{2!}a^5b^2+
\dfrac{7\cdot6\cdot5}{3!}a^4b^3+\\
\dfrac{7\cdot6\cdot5\cdot4}{4!}a^3b^4+
\dfrac{7\cdot6\cdot5\cdot4\cdot3}{5!}a^2b^5+
\dfrac{7\cdot6\cdot5\cdot4\cdot3\cdot2}{6!}a^1b^6+\\
\dfrac{7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{7!}a^0b^7
\\\\=
a^7+7a^6b+21a^5b^2+35a^4b^3+35a^3b^4+21a^2b^5+7ab^6+b^7
\end{array}