Question

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

Answer 1

\(=-4.\left(x^3+3x^2.3y+3x.\left(3y\right)^2+\left(3y\right)^3\right)+\left(x^2-y^2\right)-\left(\left(2x\right)^3-3.\left(2x\right)^2.y+3.2x.y^2-y^3\right)\)

\(=-4\left(x^3+9x^2y+27xy^2+27y^3\right)+x^2-y^2-\left(8x^3-12x^2y+6xy^2-y^3\right)\)

\(=-4x^3-36x^2y-108xy^2-108y^3+x^2-y^2-8x^3+12x^2y-6xy^2+y^3\)

\(=-4x^3-8x^3-36x^2y+12x^2y-108xy^2-6xy^2-108y^3+y^3+x^2-y^2\)

\(=-12x^3-24x^2y-114xy^2-107y^3+x^2+y^2\)