I'm having a lot of issues with this question. Ive done problems where I need to find the coefficient or the constant using the binomial theorem but I'm not sure how to even begin doing this. I looked online and can't find anything similar. Any help would be appreciated, I really want to understand this problem so I'm not looking for just the solution.
Simplify the following 2 sums:
a) $${n \choose 0}+7{n \choose 1}+7^2{n \choose 0}+\dots+7^n{n \choose n}$$
b) $$ 7^n{n \choose 0}-7^{n-1}{n \choose 1}+7^{n-2}{n \choose 2}+\dots+(-1)^n{n \choose n} $$
Hint: $$(1+x)^n=\binom{n}{0}+x\binom{n}{1}+x^2\binom{n}{2}+\dots+x^n\binom{n}{n}$$ $$(x+y)^n=x^n\binom{n}{0}+x^{n-1}y\binom{n}{1}+x^{n-2}y^2\binom{n}{2}+\dots+y^n\binom{n}{n}$$ where $n\in\mathbb{N}$.