`a)x(x-1)(x+1)-(x+1)(x²-x+1)`
`=x(x²-1)-(x³+1)`
`=x³-x-x³-1`
`=-x-1`
`b)-x(x+2)²+(2x+1)²+(x+3)(x²-3x+9)-1`
`=-x(x²+4x+4)+4x²+4x+1+x³+27-1`
`=-x³-4x²-4x+4x²+4x+1+x³+27-1`
`=(-x³+x³)+(-4x²+4x²)+(-4x+4x)+(1+27-1)`
`=27`
`d)(x-1)(x-2)(1+x+x²)(4+2x+x²)`
`=[(x-1)(1+x+x²)][(x-2)(4+2x+x²)]`
`=[(x-1)(x²+x+1)][(x-2)(x²+2x+4)]`
`=(x³-1³)(x³-2³)`
`=(x³-1)(x³-8)`
`=x^6-8x³-x³+8`
`=x^6-9x³+8`
`f)(x-3)(x²+3x+9)+x(x+2)(2-x)`
`=x³-3³+x(2+x)(2-x)`
`=x³-27+x(4-x²)`
`=x³-27+4x-x³`
`=(x³-x³)+4x-27`
`=4x-27`
`g)6(x+1)²-2(x+1)³+2(x-1)(x²+x+1)`
`=6(x²+2x+1)-2(x³+3x²+3x+1)+2(x³-1)`
`=6x²+12x+6-2x³-6x²-6x-2+2x³-2`
`=(-2x³+2x³)+(6x²-6x²)+(12x-6x)+(6-2-2)`
`=6x+2`