Transform term for induction proof Could you help me to mathematically show that these two terms are the same (they are). This is the last (but probably the most important :( ) step of an induction proof.
$$First:  \frac{(n+1)(n+2)(2(n+1)+7)}{6}$$
$$Second:  \frac{n(n+1)(2n+7)+6(n+1)(n+3)}{6}$$
Thank you! :)

A (hopefully) more elegant variant:
Once you've factored out $\dfrac{n+1}6$, there remains


*

*$n(2n+7)+6(n+3)=n\bigl(2(n+3)+1\bigr)+6(n+3)=\color{red}{2(n+3)^2+n}$.

*$(n+2)\bigl(2(n+1)+7\bigr)=\bigl((n+3)-1\bigr)\bigl(2(n+3)+3\bigr)=2(n+3)^2+(3-2)(n+3)-3=\color{red}{2(n+3)^2+n}.$

