Question

rút gọn đa thức với đa thức

(x-y).(x^2+xy+y^2)-(x+y).(x^2-xy+y^2)

Answer 1

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

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

Answer 2

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

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

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