Hey! Okay, so for that second question, as I alluded, you are equating coefficients:
We seek coefficients of some random term, x^r. On the left, we are pairing off terms which will multiply to give a power of x^r, for example, the coefficient of x^r will pair with a constant term. The coefficient of x^(r-2) will pair with the coefficient of x^2 in the other bracket. Etc. Taking these product of these coefficients gives one side of the relationship in the question. The other side falls straight out of the RHS, by considering the coefficient of x^r.
The bottom one stumped me for a bit, but it is similar! The RHS suggests that we consider the following identity:
This time, we are considering coefficients of x^n.
We apply this logic to all the pairs in the LHS of the relationship, and by equating coefficient, the result comes out!
This is a
really tricky one to explain, a super tough question. Read this a few times, work with me if you can, see if you follow my reasoning, and of course ask any questions you might have