Question

How do you use the Binomial Theorem to expand `(2x−1)^4`?

Answer 1

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

Explanation:

Given: `(2x-1)^4`

We can say that:
`(2x)^4(-1)^0+(2x)^3(-1)^1+(2x)^2(-1)^2+(2x)^1(-1)^3+(2x)^0(-1)^4=`

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

However we are not quite done, we need the coefficients in front of each term, I would use combinations unless you really want to use Pascal's triangle, which you can since this a small exponent.

Using pascal's triangle:
For row 4: the coefficients are `1, 4, 6, 4, 1`

`1*16x^4+4*-8x^3+6*4x^2+4*-2x+1*1`

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