Question

因式分解：（x²+1)²-x²+x(x-2)(x²+x+1)

快啊在线等我要疯了

Answer 1

原式=x^4+x²+1+x(x-1)(x²+x+1)-x(x²+x+1)
=x(x-1)(x²+x+1)+x^4-x³-x+1
=x(x-1)(x²+x+1)+x³(x-1)-(x-1)
=(x-1)[x(x²+x+1)+(x-1)(x²+x+1)]
=(x-1)(x²+x+1)(2x-1)
解法2
原式=(x²+1+x)(x²+1-x)+x(x-2)(x²+x+1)
=(x²+x+1)(x²+1-x+x²-2x)
=(x²+x+1)(2x²-3x+1)
=(x²+x+1)(x-1)(2x-1)

Answer 2

x-1)(x-2)-2(2-x)²
= (x-1)(x-2)-2(x-2)²
= （x-2)(x-1-2(x-2))
= (x-2)(x-1-2x-4)
= (x-2)(-x-5)
= -(x-2)(x+5)