分解 2x^3-4x^2y-x^2z+2xy^2+2xyz-y^2z求过程

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分解 2x^3-4x^2y-x^2z+2xy^2+2xyz-y^2z求过程

分解 2x^3-4x^2y-x^2z+2xy^2+2xyz-y^2z求过程
分解 2x^3-4x^2y-x^2z+2xy^2+2xyz-y^2z求过程

分解 2x^3-4x^2y-x^2z+2xy^2+2xyz-y^2z求过程
2x^3-4x^2y-x^2z+2xy^2+2xyz-y^2z
=(2x^3-4x^2y+2xy^2)-(x^2z-2xyz+y^2z)
=2x(x^2-2xy+y^2)-z(x^2-2xy+y^2)
=2x(x-y)^2-z(x-y)^2
=(x-y)^2(2x-z)

2x³-4x²y-x²z+2xy²+2xyz-y²z
=﹙2x³-4x²y+2xy²﹚-﹙x²z-2xyz+y²z﹚
=2x﹙x²-2xy+y²﹚-z﹙x²-2xy+y²﹚
=﹙2x-z﹚﹙x²-2xy+y²﹚
=﹙2x-z﹚﹙x-y﹚²

2x³-4x²y-x²z+2xy²+2xyz-y²z
=(2x³-4x²y+2xy²)-(x²z-2xyz+y²z)
=2x(x²-2xy+y²)-z(x²-2xy+y²)
=2x(x-y)²-z(x-y)²
=(x-y)²(2x-z)