Answer
$x^8+8x^7y+28x^6y^2+56x^5y^3+70x^4y^4+
56x^3y^5+28x^2y^6+8xy^7+y^8
$
Work Step by Step
Using the Binomial Formula, the expression $
(x+y)^8
$ expands to
\begin{array}{l}
x^8b^0+
\dfrac{8}{1!}a^7b^1+
\dfrac{8\cdot7}{2!}a^6b^2+
\dfrac{8\cdot7\cdot6}{3!}a^5b^3+
\dfrac{8\cdot7\cdot6\cdot5}{4!}a^4b^4+\\
\dfrac{8\cdot7\cdot6\cdot5\cdot4}{5!}a^3b^5+
\dfrac{8\cdot7\cdot6\cdot5\cdot4\cdot3}{6!}a^2b^6+
\dfrac{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2}{7!}a^1b^7+\\
\dfrac{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{8!}a^0b^8
\\\\=
x^8+8x^7y+28x^6y^2+56x^5y^3+70x^4y^4+\\56x^3y^5+28x^2y^6+8xy^7+y^8
\end{array}
