`***`Lời giải`***`
a)
`x^2(x-2y)-y^2(y-2x)`
`=x^3-2x^2y-y^3+2xy^2`
`=(x^3-y^3)+(-2x^2y+2xy^2)`
`=(x-y)(x^2+xy+y^2)-2xy(x-y)`
`=(x-y)(x^2+xy+y^2-2xy)`
`=(x-y)(x^2-xy+y^2)`
b)
`x^8+x^4+1`
`=(x^8+2x^4+1)-x^4`
`=(x^4+1)^2-(x^2)^2`
`=(x^4+1+x^2)(x^4+1-x^2)`
c)
`(x^2-2x)^3-3x^2+6x+2`
`=x^6-6x^5+12x^4-8x^3-3x^2+6x+2`
`=x^6-2x^5-4x^5+8x^4+2x^4+2x^4-8x^3-4x^3+4x^3-8x^2+4x^2+x^2-2x+8x+2`
`=(x^6-2x^5+2x^4)+(-4x^5+8x^4-8x^3)+(2x^4-4x^3+4x^2)+(4x^3-8x^2+8x)+x^2-2x+2`
`=x^4(x^2-2x+2)-4x^3(x^2-2x+2)+2x^2(x^2-2x+2)+4x(x^2-2x+2)+x^2-2x+2`
`=(x^2-2x+2)(x^4-4x^3+2x^2+4x+1)`
`=(x^2-2x+2)(x^4-2x^3-2x^3-x^2-x^2+4x^2+2x+2x+1)`
`=(x^2-2x+2)[(x^4-2x^3-x^2)+(-2x^3+4x^2+2x)-x^2+2x+1]`
`=(x^2-2x+2)[x^2(x^2-2x-1)-2x(x^2-2x-1)-(x^2-2x-1)]`
`=(x^2-2x-1)(x^2-2x-1)(x^2-2x+2)`
`=(x^2-2x-1)^2(x^2-2x+2)`
