Question

Coefficient of x^2 in expansion of the binomial theorem (2x-1)^4 show your work

Answer 1

24

Explanation:

If you use Pascal's triangle, which I did, you will look at the 5th row of the triangle which contains the numbers 1, 4, 6, 4, 1

If we expand using a = 2x and b = -1, then the expansion looks like this:

`1(2x)^4(-1)^0+4(2x)^3(-1)^1+6(2x)^2(-1)^2+4(2x)^1(-1)^3+1(2x)^0(-1)^4`

If you simplify all that down by multiplying, you'll get

`16x^4-32x^3+24x^2-8x+1`

If you don't know how to use Pascal's triangle, you need to learn. It's so very cool!