Question

rút gọn biểu thức: (x+y)^3-(x-y)^3 giúp với ạ

Answer 1

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

\(=x^3+3x^2y+3xy^2+y^3-(x^3-3x^2y+3xy^2-y^3)\)

\(=6x^2y+2y^3\)

Answer 2

Cách khác:

Ta có: \(\left(x+y\right)^3-\left(x-y\right)^3\)

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

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

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

\(=6x^2y+2y^3\)