Question

(6m - n)^3

Please show your work!

Answer 1

`(6m - n) {}^(3) \\ (6m - n) {}^(2) (6m - n) \\ (36m {}^(2) - 12mn + n {}^(2) )(6m - n) \\ 216m {}^(3) - 36m {}^(2) n - 72m {}^(2) n + 12mn {}^(2) + 6mn {}^(2) - n {}^(3)`

`(6m - n) {}^(3) = 216m {}^(3) - 108m {}^(2) n + 18mn {}^(2) - n {}^(3) \\`

You could also expand using the Binomial Theorem, but that's a bit advanced

`(6m - n) {}^(3) ={3}C_(0)(6m) {}^(3)( - n ){}^(0) + 3C_(1)(6m) {}^(2)( - n ){}^(1) + 3C_(2)(6m) {}^(1) ( - n) {}^(2) + 3C_(3)(6m) {}^(0) ( - n) {}^(3)`