Youdounderstand that you're working towards the final line being > (k + 1)^2? So the k^2 gets replaced with (k - 1)^2 + 2k -1 because (k - 1)^2 is bigger than 2 for k > 4 and so you can write the second last line, which will give you the final line ......

It's a trick that once seen youmemoriseand then learn togeneralise- as in the second problem, where you need to work towards the final line being > (k + 1)^3.