Question

(x + 2)^(4) = x^(4) + 8x^(3) +... Use the Binomial Theorem to complete the binomial expansion. Enter only the next three terms; use the ^ key for exponents, example: 10x^2+20x+30.

Answer 1

@Hero

Answer 2

\[\begin{align*}(x+2)^4&=\sum_{k=0}^{4}\begin{pmatrix}4\\k\end{pmatrix}x^{4-k}2^{k}\\
&=\begin{pmatrix}4\\0\end{pmatrix}x^{4}2^{0}+\begin{pmatrix}4\\1\end{pmatrix}x^{3}2^{1}+\begin{pmatrix}4\\2\end{pmatrix}x^{2}2^{2}+\begin{pmatrix}4\\3\end{pmatrix}x^{1}2^{3}+\begin{pmatrix}4\\4\end{pmatrix}x^{0}2^{4}
\end{align*}\]
You probably know this, but
\[\begin{pmatrix}n\\k\end{pmatrix}=\frac{n!}{k!(n-k)!}\]