Question on mathematical induction which involves factorial and inequality.

Question

The image shows the mark scheme for mathematical induction question. I do not understand how you know $(2k)!$ is more than $(k!)^2 2^k$ ($2$ lines below consider $P(k+1)$. Can someone explain it to me please?

Answer 1

That is the induction hypothesis, we assume $P(k)$ is true: that is $(2k)! > (k!)^2 2^k$ is true.