Question

How do you expand `(2m-1)^4`?

Answer 1

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

Explanation:

Using Pascals triangle . The row for`(x+y)^4`

is `1" "4" "6" " 4" " 1" "`

These are the coefficients for each of the respective terms.

the terms themselves are various powers of the first and second terms of the brackets. Start with the first term `2m` to the power of `4` and the second to the power `0` then reduce the powers of the first by `1` and increase the power of the second by 1 , making sure their powers always sum to `4` (in this case).

we have then

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

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