Question

(2x-1)^4

What is the coefficient of x^2?

Answer 1

It would be a good idea if you familiarize yourself with Pascal's Triangle,
the 4th row has values 1 4 6 4 1

so (2x-1)^4
= (2x)^4 + 4(2x)^3 (-1) + 6(2x)^2 (-1)^2 + 4(2x) (-1)^3 + (-1)^4


the term that will yield x^2 is 6(2x)^2(-1)^2
= 24x^2

confirmed by Wolfram:

http://www.wolframalpha.com/input/?i=expand+%282x+-+1%29%5E4