Question

How do you expand `(2b-x)^4`?

Answer 1

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

Explanation:

Using Pascal's triangle for the coefficients of `(x+a)^4` to be 1,4,6,4,1, the expansion of `(2b-x)^4` would be

`(2b)^4 +4 (2b)^3 (-x) +6 (2b)^2 (-x)^2 +4 (2b) (-x)^3 + (-x)^4`

On simplification it becomes

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