Question

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?

Answer 1

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.

Answer 2

SOLUTION: (3m - 4n)(9m^2 + 12mn + 16n^2)

Explanation:

27m^3 - 64n^3

(3m - 4n) ((3m)^2 + (3m)(4n) + (4n)^2)

SOLUTION: (3m - 4n)(9m^2 + 12mn + 16n^2)

** I think you might have switched added instead of subtracted.