simplify (3x+4y)³-(3x-4y)³-216x²y

Question

May be the answer is 128y² .I dont know how to solve it

Answer 1

(3x+4y)^3 - (3x - 4y)^3 - 216x^2y

Pascal's triangle, 4th row, 1 3 3 1

27x^3 + 108x^2y + 144xy^2 + 64y^3 - (27x^3 - 108x^2y + 144xy^2 - 64y^3) - 216x^2y

27x^3 - 27x^3 + 108x^2y + 108x^2y - 216x^2y +144xy^2 - 144xy^2 + 64y^3 + 64y^3

128y^3

Answer 2

Eqn (3x + 4y)^3 - (3x - 4y)^3 - 216x^2y

from 

(a^3 + b^3) = a^3 + b^3 + 3ab(a + b)

=27x^3 + 64y^3 + 36xy(3x + 4y) - { 27x^3 - 64y^3 - 36xy(3x - 4y)

=27x^3 + 64y^3 + 108x^2y + 144xy^2 - 27x^3 + 64y^3 + 108x^2y - 144xy^2 - 216x^2y

=128y^3

therefore 

 (3x + 4y)^3 - (3x - 4y)^3 - 216x^2y = 128y^3