Ta có:
\(VT=\left(x+y+z\right)^3\)
\(=\left[\left(x+y\right)+z\right]^3\)
\(=\left(x+y\right)^3+z^3+3z\left(x+y\right)\left(x+y+z\right)\)
\(=x^3+y^3+z^3+3z\left(x+y\right)\left(x+y+z\right)+3xy\left(x+y\right)\)
\(=x^3+y^3+z^3+3\left(x+y\right)\left[\left(x+y+z\right)z+xy\right]\)
\(=x^3+y^3+z^3+3\left(x+y\right)\left[\left(xy+xz\right)+\left(yz+z^2\right)\right]\)
\(=x^3+y^3+z^3+3\left(x+y\right)\left[x\left(y+z\right)+z\left(y+z\right)\right]\)
\(=x^3+y^3+z^3+3\left(x+y\right)\left(y+z\right)\left(z+x\right)\) (đpcm)
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