Question

(3x + y)^3 + (3x - y)^3

Answer 1

a^3+b^3) = (a+b)(a^2-ab+b^2)

so,
(3x+y)^3 + (3x-y)^3
= ((3x+y)+(3x-y))((3x+y)^2-(3x+y)(3x-y)+(3x-y)^2)
= (6x)(9x^2+6xy+y^2-9x^2+y^2+9x^2-6xy+y^2)
= (6x)(9x^2+3y^2)
= 18x(3x^2+y^2)