`(x-1)^4-2(x^2-2x+1)^3+1`
`=(x-1)^4-2[(x-1)^2]^3+1`
`=(x-1)^4-2(x-1)^6+1`
Đặt: `(x-1)^2=a(a>=0)`
`=a^2-2a^3+1`
`=-2a^3+a^2+1`
`=-2a^3+2a^2-a^2+1`
`=-2a^2(a-1)-(a^2-1)`
`=-2a^2(a-1)-(a-1)(a+1)`
`=(a-1)(-2a^2-a-1)`
Tại `a^2=[(x-1)^2]^2=(x-1)^4`
`=[(x-1)^2-1][-2(x-1)^4-(x-1)^2-1]`
`=(x^2-2x)[(x-1)^2[-2(x-1)^2-1]-1]`
`=x(x-2)[(x^2-2x+1)[-2(x^2-2x+1)-1]-1]`
`=x(x-2)[(x^2-2x+1)(-2x^2+4x-2-1)-1]`
`=x(x-2)(-2x^4+4x^2-3x^2+4x^2-8x^2+6x-2x^2+4x-3-1)`
`=x(x-2)(-2x^4+8x^2-13x^2+10x-4)`
