Question

8x^3-y^3-6xy(2x-y)

Answer 1

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

\(=\left(2x-y\right)\left(4x^2+2xy+y^2\right)-6xy\left(2x-y\right)\)

\(=\left(2x-y\right)\left(4x^2-4xy+y^2\right)\)

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

Answer 2

\(8x^3-y^3-6xy\left(2x-y\right)\)
\(=\left[\left(2x\right)^3-y^3\right]-6xy\left(2x-y\right)\)
\(=\left(2x-y\right)\left[\left(2x\right)^2+2x.y+y^2\right]-6xy\left(2x-y\right)\)
\(=\left(2x-y\right)\left(4x^2+2xy+y^2-6xy\right)\)
\(=\left(2x-y\right)\left(4x^2-4xy+y^2\right)\)
\(=\left(2x-y\right)\left(2x-y\right)^2\)
\(=\left(2x-y\right)^3\)