a) Ta có: \(VP=x^4-y^4\)
\(=\left(x^2-y^2\right)\left(x^2+y^2\right)\)
\(=\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\)
\(=\left(x^3+x^2y+xy^2+y^3\right)\left(x-y\right)=VP\)(đpcm)
b) Ta có: \(VT=\left(a-b\right)\left(a^2+b^2+ab\right)-\left(a+b\right)\left(a^2+b^2-ab\right)\)
\(=a^3-b^3-\left(a^3+b^3\right)\)
\(=a^3-b^3-a^3-b^3\)
\(=-2b^3=VP\)(đpcm)
a, \(\left(x^3+x^2y+xy^2+y^3\right)\left(x-y\right)=x^4-y^4\)
Ta có: VT: \(\left(x^3+x^2y+xy^2+y^3\right)\left(x-y\right)\)
= \(\left[\left(x^3+y^3\right)+\left(x^2y+xy^2\right)\right]\left(x-y\right)\)
= \(\left(x+y\right)\left(x^2-xy+y^2\right)+xy\left(x+y\right)\left(x-y\right)\)
= \(\left(x+y\right)\left(x^2-xy+y^2+xy\right)\left(x-y\right)\)
=\(\left(x+y\right)\left(x-y\right)\left(x^2+y^2\right)\)
= \(\left(x^2-y^2\right)\left(x^2+y^2\right)\)
= \(x^4+x^2y^2-x^2y^2-y^4\)
= \(x^4-y^4\) (VP) đpcm
