Further maths help - proof by induction (divisibility)

I need help on what to do next

Ok so notice that from your last line you can say:

$10(11^{k+1}) + 143(12^{2k-1}) = 10(11^{k+1}) + 10(12^{2k-1}) + 133(12^{2k-1})$.

What do you notice from here??

Ok so 10 was a common factor so i factored it out.
After that, i needed to add f(k) after to the equation, which i did. I looked blankly at my paper when i realised that 10(11^k+1 + 12^2k-1) is equal to the assumtion step equation thingy. Therefore, i got 10f(k) + f(k) + 133(12^2k-1). I think im done?? my final answer is there on the paper

Yeah heres the pic

Yes you are done with the algebra and whatnot. You just need a closing statement to complete the proof.

The closing statement is so damn flipping long. How am i meant to remember the statement for normal induction and divisibility induction? It's like revising for gcse english quotes lol