<s>[INST] Process for $(k+1)^3$? I've mentioned in previous questions that I have a hard time with simplifying algebraic equations. 
For this equation, I assumed we would first put the equation into easier to read form:
$(k+1)(k+1)(k+1)$
Then apply FOIL to the first two:
EDIT: $(k^2+2k+1)(k+1)$
Although this is where I'm stuck. Any help is appreciated. 
With all your help my answer is:
$k^3+3k^2+3k+1$
Thanks. 
 [/INST] Use the distributive law (after correcting your first multiplication):
$$(k^2+2k+1)(\color{red}{k}+\color{blue}{1})=(k^2+2k+1)\cdot\color{red}{k}+(k^2+2k+1)\cdot\color{blue}{1}\;.$$
Now $(k^2+2k+1)\cdot k=k^3+2k^2+k$, and $(k^2+2k+1)\cdot 1=k^2+2k+1$, so all that’s left is to add the two polynomials:
$$\begin{align*}
(k^3+2k^2+k)+(k^2+2k+1)&=k^3+(2k^2+k^2)+(k+2k)+1\\
&=k^3+3k^2+3k+1\;.
\end{align*}$$
You can also organize this calculation like a pencil-and-paper multiplication:
$$\begin{array}{r}
&&k^2&+&2k&+&1\\
&&&&k&+&1\\ \hline
&&k^2&+&2k&+&1\\
k^3&+&2k^2&+&k\\ \hline
k^2&+&3k^2&+&3k&+&1
\end{array}$$
</s>