因式分解 (x^2-y^2)(x-y)^2-(x-y)^4

如题

(x^2-y^2)(x-y)^2-(x-y)^4
=(x-y)^2[(x^2-y^2)-(x-y)^2]
=(x-y)^2(x^2-y^2-x^2+2xy-y^2)
=(x-y)^2(-2y^2+2xy)
=2y(x-y)^2(x-y)
=2y(x-y)^3
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第1个回答  2009-06-01
(x^2-y^2)(x-y)^2-(x-y)^4

=(x+y)(x-y)^3-(x-y)^4

=[(x+y)-(x-y)](x-y)^3

=2y(x-y)^3

因式分解 (x^2-y^2)(x-y)^2-(x-y)^4
(x^2-y^2)(x-y)^2-(x-y)^4 =(x-y)^2[(x^2-y^2)-(x-y)^2]=(x-y)^2(x^2-y^2-x^2+2xy-y^2)=(x-y)^2(-2y^2+2xy)=2y(x-y)^2(x-y)=2y(x-y)^3

初二的因式分解题:(x^2-y^2)(x+y)^2-(x-y)^4
=(x-y)[(x+y)^2*(x+y)-(x-y)^2*(x-y)]=(x-y)[(x^3+3x^2y+3xy^2+y^3)-(x^3-3x^2y+3xy^2-y^3)]=(x-y)(2y^3+6x^2y)=-2y^4+6x^3y+2xy^3-6x^2y^2

x^2-y^2-x-y 因式分解
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因式分解(x^2-y^2)(x^4+x^2y^2+y^4)
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x^2-y^2-(x+y)^2,因式分解
x^2-y^2-(x+y)^2 =(x-y)(x+y)-(x+y)^2 =(x-y-x-y)(x+y)=-2y(x+y)

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