Question

Cho x-y=1 Tính 2(\(x^3-y^3\))-(\(x^2+y^2\)+4xy)

Answer 1

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

\(=2+6xy-1-6xy=1\)

Answer 2

\(2\left(x^3-y^3\right)-\left(x^2+y^2+4xy\right)\)

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

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

\(=x^2+y^2-2xy\)

\(=\left(x-y\right)^2=1\)