Question

Chứng minh : ( \(x^3+x^2y+xy^2+y^3\)).(x - y) = \(x^4-y^4\)

Answer 1

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

Answer 2

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

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

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

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

\(=x^4-y^4=VP\) (ĐPCM)

Answer 3

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

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

\(=x^4-y^4=VP\)

Vậy \(\left(x^3+x^2y+xy^2+y^3\right)\cdot\left(x-y\right)=x^4-y^4\) (đpcm)