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x四次方-4 x平方+4x-1
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原式=(x^4-1)-4x²+4x
=(x²+1)(x+1)(x-1)-4x(x-1)
=(x-1)(x³+x²+x+1-4x)
=(x-1)[(x³-x)+(x²-x)-(x-1)]
=(x-1)[x(x+1)(x-1)+x(x-1)-(x-1)]
=(x-1)²(x²+x+x-1)
=(x-1)²(x²+2x-1)
=(x²+1)(x+1)(x-1)-4x(x-1)
=(x-1)(x³+x²+x+1-4x)
=(x-1)[(x³-x)+(x²-x)-(x-1)]
=(x-1)[x(x+1)(x-1)+x(x-1)-(x-1)]
=(x-1)²(x²+x+x-1)
=(x-1)²(x²+2x-1)
来自:求助得到的回答
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