27m^3+64n^3

Answer sheet says it is (3m+4n) (9m^2-12mn+16n^2) can someone tell me where they got the "-12mn" from?

27m^3+64n^3 is an example of the sum of two cubes.

There's a factoring formula for that: a^3 + b^3 = (a + b) (a^2 - ab + b^2.

Thus, 27m^3+64n^3 = (3m + 4n) (9m^2 - 12mn + 16n^2).

Could also find this out by dividing 3m+4n into 27m^3+64n^3.