F4 maths:factorization urgent!

x^4-y^4
(x^2+y^2)(x^2-y^2)
(x^2+y^2)(x+y)(x-y)




x^3y-x^2y-xy^3+y^3
x^2y(x-1)-y^3(x-1)
(x-1)(x^2y-y^3)
(x-1)y(x^2-y^2)
y(x-1)(x+y)(x-y)

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好好人呀你！THX!!!

factorize x^4- y^4 and x^3 y – x^2 y -x y^3 + y^3
x^4 - y^4
= (x^2 - y^2)(x^2 + y^2)
= (x-y)(x+y)(x^2 + y^2)
x^3 y – x^2 y -x y^3 + y^3
= y(x^3 - x^2 - x + y^2)
= y[x(x^2 - 1) + (y-x)(y+x)]
= y[x(x-1)(x+1)+(y-x)(y+x)]


2010-04-15 20:59:14 補充：
x^3 y – x^2 y -x y^3 + y^3
= y[x^3 - y^3] - y[x^2 - y^2]
= y(x-y)(x^2 - xy + y^2) - y(x-y)(x+y)
= y(x-y)(x^2 - xy + y^2 - x - y)