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> Prove that if $h > -1$, then $1 + nh ≤ (1+h^n)$ for all nonnegative integers $n$.
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I've read several solutions and I'm still totally lost on how to go about this. 

I have the **inductive hypothesis**: $1+kh ≤ (1+h)^{k}$.

And that we want to **prove**: $1+(k+1)h ≤ (1+h)^{k+1}$.

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From here, I found various first steps that I don't understand. Examples:

1. $(1+h)(1+kh) ≤ (1+h)^k(1+h)$. How did they get the left side?
2. $1 + kh + h ≤ (1 + h)(k + kh)$. How did they arrive at the right side?