\(x+y+z+t=0\Rightarrow t=-\left(x+y+z\right)\)
Ta có:
\(VT=x^3+y^3+z^3+t^3=x^3+y^3+z^3-\left(x+y+z\right)^3\)
\(=x^3+y^3+z^3-\left[x^3+y^3+z^3+3\left(x+y\right)\left(y+z\right)\left(z+x\right)\right]\)
\(=-3\left(x+y\right)\left(y+z\right)\left(z+x\right)\)
\(VP=3\left[xy+z\left(x+y+z\right)\right]\left(z-x-y-z\right)=3\left(xy+yz+zx+z^2\right)\left(-x-y\right)\)
\(=-3\left(y+z\right)\left(z+x\right)\left(x+y\right)\)
Do VT = VP nên ta có đpcm.
