Part (a)
\begin{align}
(a-b)(a^2+ab+b^2)&=a^3+a^2b+ab^2-a^2b-ab^2-b^3\\
&=a^3-b^3
\end{align}
Part (b)
Using the similar factorisation for a^3+b^3 :
\begin{align}
\frac{2016^3+2015^3}{2016^2-2015^2}&=\frac{(2016+2015)(2016^2-2016\times 2015+2015^2)}{(2016+2015)(2016-2015)}\\
&=\frac{2016^2-2016\times 2015+2015^2}{2016-2015}\\
&=2016^2-2016\times 2015+2015^2\\
&=2016^2-2\times 2016\times 2015+2015^2+2016\times 2015\\
&=(2016-2015)^2+2016\times 2015\\
&=1+4062240\\
&=4062241
\end{align}
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