Question

Answer 1

\(\left(2x+y\right)^3-6\left(2x+y\right)^2x+12\left(2x+y\right)x^2-8x^3\)

\(=\left(2x+y\right)^3-3\cdot2x\cdot\left(2x+y\right)^2+3\cdot\left(2x+y\right)\cdot\left(2x\right)^2-\left(2x\right)^3\)

\(=\left[\left(2x+y\right)-2x\right]^3\)

\(=\left(2x+y-2x\right)^3\)

\(=y^3\)

Answer 2

\(\left(2x+y\right)^3-6\left(2x+y\right)^2x+12\left(2x+y\right)x^2-8x^3\\ =8x^3+12x^2y+6xy^2+y^3-6x\left(4x^2+4xy+y^2\right)+24x^3+12x^2y-8x^3\\ =8x^3-8x^3+12x^2y+6xy^2+y^3-24x^3-24x^2y-6xy^2+24x^3+12x^2y\\ =y^3\)