Question

因式分解(1+y)2-2x^2(1+y^2)+x^4 (1-y)^2 ..

Answer 1

(1+y)2-2x^2(1+y^2)+x^4 (1-y)^2
=(1+y)²-2x²(1-y²)-4x²y²+x^4 (1-y)²
=(1+y)²-2x²(1-y²)+x^4 (1-y)²-4x²y²
=[(1+y)-x²(1-y)]²-4x²*y²
=(1+y-x²+x²y)²-(2xy)²
=(1+y+2xy-x²+x²y)(1+y-2xy-x²+x²y)
=[1-x²+y(1+2x+x²)][1-x²+y(1-2x+x²)]
=[(1+x)(1-x)+y(1+x)²][(1+x)(1-x)+y(1-x)²]
=(1+x)(1-x+y+xy)(1-x)(1+x+y-xy)

好复杂...

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