Answer and step-by-step explanation:
To find the cube of the given binomial, expand it first.
(6m - 3n)^2
= (6m - 3n)(6m - 3n)(6m - 3n)
Then use the FOIL method to simplify the two binomials.
(6m - 3n)(6m - 3n)
F: (6m)(6m) = 36m^2
O: (6m)(-3n) = -18mn
I: (-3n)(6m) = -18mn
L: (-3n)(-3n) = 9n^2
= 36m^2 - 36mn + 9n^2
The polynomial is now like this:
(36m^2 - 36mn + 9n^2)(6m - 3n)
Then apply the distributive property of multiplication and simplify the similar terms.
(6m)(36m^2 - 36mn + 9n^2) + (-3n)(36m^2 - 36mn + 9n^2)
= 216m^3 - 216m^2n + 54mn^2 - 108m^2n + 108mn^2 - 27n^3
= 216m^3 - 324m^2n + 162mn^2 - 27n^3
Therefore, the answer is
[tex]216m^3 - 324m^2n + 162mn^2 - 27n^3[/tex]
