Question

What is the binomial expansion of `(2x -3)^5`?

Answer 1

`32x^5-240x^4+720x^3-1080x^2+810x-243`

Explanation:

5th row of pascal's triangle:
1 5 10 10 5 1
these are the coefficients of each term

`(2x-3)^5 = 1(2x)^5(3^0) + 5(2x)^4(3^1) + 10(2x)^3(3^2) + 10(2x)^2(3^3) + 5(2x)^1(3^4) + 1(2x)^0(3^5)`

`n^0 = 1`

`(2x-3)^5 = 1(2x)^5 + 5(2x)^4(-3)^1 + 10(2x)^3(-3)^2 + 10(2x)^2(-3)^3 + 5(2x)^1(-3)^4 + 1(-3)^5`

`(2x)^5 = 32x^5`
`5(2x)^4(-3)^1 = 16x^4*-3 = -240x^4`
`10(2x)^3(-3)^2 = 8x^3*9 = 720x^3`
`10(2x)^2(-3)^3 = 4x^2*-27 = -1080x^2`
`5(2x)^1(-3)^4 = 2x*81 = 810x`
`3^5 = -243`

sum:
`32x^5-240x^4+720x^3-1080x^2+810x-243`