分解因式(x^2 y^2
分解因式(x^2 y^2-2x 1)^2-(4y-4xy)(x^2-y^2-2x 1)分解因式(x^2+y^2-2x+1)^2-(4y-4xy)(x^2-y^2-2x+1) 求助,kkkkkkkk
(x^2+y^2-2x+1)^2-(4y-4xy)(x^2-y^2-2x+1)
=(x^2+y^2-2x+1)^2-4y(1-x)(x^2-y^2-2x+1)
=[(x-1)^2+y^2]^2+4y(x-1)[(x-1)^2-y^2]
=[(x-1)^2+y^2]^2+4y(x-1)[(x-1)^2+y^2-2y^2]
=[(x-1)^2+y^2]^2+2*2y(x-1)[(x-1)^2+y^2]+4y^2(x-1)^2
-4y^2(x-1)^2-8y^3(x-1)
=[(x-1)^2+y^2+2y(x-1)]^2-4y^2(x-1)(x-1+2y)
=[(x-1)(x-1+2y)+y^2]^2-4y^2(x-1)(x-1+2y)
=[(x-1)(x-1+2y)]^2+2y^2(x-1)(x-1+2y)+y^4--4y^2(x-1)(x-1+2y)
=[(x-1)(x-1+2y)]^2-2y^2(x-1)(x-1+2y)+y^4
=[(x-1)(x-1+2y)+y^2]^2
=[(x-1)^2+2y(x-1)+y^2]^2
={[(x-1)+y]^2}^2
=(x+y-1)^4
。
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