We started doing binomial expansions today and I really do not get it at all. I get that in the form:

(a+b)^n the exponents on a decrease and on b they increase and that there are n + 1 terms and you use pascal's triangle to get the terms but I don't quite get how to simplify what I come up with.

E.g. (3x+4a)^5

= 3x^5 + 5(3x^4+4a^1) + 10(3x^3+4a^2) + 10(3x^2+4a^3) + 5(3x+4a^4) + (4a^5)

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

This is as far as I get but I don't get how to simplify it. Any help would be super awesome. I don't even know if that is correct.

Thanks.