x3+y3+z3+(x+y)3+(y+z)3+(z+x)3因式分解

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x3+y3+z3+(x+y)3+(y+z)3+(z+x)3因式分解x3+y3+z3+(x+y)3+(y+z)3+(z+x)3因式分解x3+y3+z3+(x+y)3+(y+z)3+(z+x)3因式分解x

x3+y3+z3+(x+y)3+(y+z)3+(z+x)3因式分解
x3+y3+z3+(x+y)3+(y+z)3+(z+x)3因式分解

x3+y3+z3+(x+y)3+(y+z)3+(z+x)3因式分解
x^3+y^3+z^3+(x+y)^3+(y+z)^3+(z+x)^3
=[x^3+(y+z)^3]+[y^3+(z+x)^3]+[z^3+(x+y)^3]
=(x + y + z) (x^2 - x y + y^2 - x z + 2 y z + z^2)+(x + y + z) (x^2 - x y + y^2 + 2 x z - y z + z^2)+(x + y + z) (x^2 + 2 x y + y^2 - x z - y z + z^2)
=3 (x + y + z) (x^2 + y^2 + z^2)