因式分解(x+y+z)3-x3-y3-z3

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

因式分解(x+y+z)3-x3-y3-z3
(x+y+z)^3-x^3-y^3-z^3
=3yx^2+3xy^2+3xz^2+3yz^2+3zx^2+3zy^2+6xyz
=3xy(x+y)+3z^2(x+y)+3z(x^2+y^2+2xy)
=3xy(x+y)+3z^2(x+y)+3z(x+y)^2
=3(x+y)[xy+z^2+z(x+y)]
=3(x+y)[x(y+z)+z(y+z)]
=3(x+y)(x+z)(y+z)

(x+y+z)3-x3-y3-z3
=(x+y+z)3-(x+y+z)3
=0

(x+y+z)3-x3-y3-z3
=3x+3y+3z-3x-3y-3z
=(3x-3x)+(3y-3y)+(3z-3z)
=0