Answer
$b^6 + 6 b^5 c + 15 b^4 c^2 + 20 b^3 c^3 + 15 b^2 c^4 + 6 b c^5 + c^6$
Work Step by Step
Using the Binomial Formula, the expression $
(b+c)^6
$ expands to
\begin{array}{l}
b^6c^0+
\dfrac{6}{1!}b^5c^1+
\dfrac{6\cdot5}{2!}b^4c^2+
\dfrac{6\cdot5\cdot4}{3!}b^3c^3+
\dfrac{6\cdot5\cdot4\cdot3}{4!}b^2c^4+\\
\dfrac{6\cdot5\cdot4\cdot3\cdot2}{5!}b^1c^4+
\dfrac{6\cdot5\cdot4\cdot3\cdot2\cdot1}{6!}b^0c^6
\\\\\\=
b^6 + 6 b^5 c + 15 b^4 c^2 + 20 b^3 c^3 + 15 b^2 c^4 + 6 b c^5 + c^6
\end{array}
