Prove using binomial theorem

Question

I understand how to use the binomial theorem how to find the coefficients of for example $(2x^2-3x^4)^6$ however how would you use it to prove something such as $(12)^4$ equals $20 736$?

Answer 1

It can't help you much but the thing you can do is to use that $12=10+2$ so you can write it like $$(10+2)^4=10^4+{4\choose 1}10^3\cdot 2+{4\choose 2}10^2\cdot 2^2+{4\choose 3}10\cdot 2^3+2^4$$