Question 391108
We could expand the expression, but there's a much faster way. If you know the binomial theorem, as well as the 5th row of Pascal's triangle, you can easily expand the expression and obtain


{{{a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5}}}


The sum of the coefficients is 1 + 5 + 10 + 10 + 5 + 1 = 32. In fact, the sum of the coefficients of any binomial expression {{{(a+b)^n}}} is {{{2^n}}}. Can you prove that it works for all positive integers n? (Hint: it relies on Pascal's triangle. Some induction would work nicely)