Algebra simplification in mathematical induction . I was proving some mathematical induction problems and came through an algebra expression that shows as follows:
$$\frac{k(k+1)(2k+1)}{6}  + (k + 1)^2$$
The final answer is supposed to be: 
$$\frac{(k+1)(k+2)(2k+3)}{6}$$
I walked through every possible expansion; I combine like terms, simplify, factor, but never arrived at the answer.
Could someone explain the steps? 

Well you can make life a lot easier for yourself by using the common factor of $k+1$. Taking this out, and also the factor of a sixth for neatness, your expression is
$$\frac 1 6 (k+1)(k(2k+1)+6(k+1))$$
Now you only have a quadratic to factor! $2k^2+7k+6$. You can use familiar methods to factor this as you seek.
