`1)(x+2)(x²-2x+4)-(15+2x³)`
`=(x+2)(x²-x.2+2²)-(15+2x³)`
`=x³+2³-15-2x³`
`=x³+8-15-2x³`
`=(x³-2x³)+(8-15)`
`=-x³-7`
`2)(3x-2y)(9x²+6xy+4y²)-(5x³-10y³)`
`=(3x-2y)[(3x)²+3x.2y+(2y)²]-5x³+10y³`
`=(3x)³-(2y)³-5x³+10y³`
`=27x³-8y³-5x³+10y³`
`=(27x³-5x³)+(-8y³+10y³)`
`=22x³+2y³`
`3)(x²+2xy-3).(-xy)`
`=-x².xy-2xy.xy-3.(-xy)`
`=-x³y-2x²y²+3xy`
`4)x²y(2x²-xy²-1)`
`=x²y.2x²-x²y.xy²-x²y.1`
`=2x^4y-x³y³-x²y`
`5)(x-7)(x-5)`
`=x(x-5)-7(x-5)`
`=x²-5x-7x+35`
`=x²-12x+35`
`6)(x-1)(x+1)(x+2)`
`=(x²-1)(x+2)`
`=x²(x+2)-1(x+2)`
`=x³+2x²-x-2`
`7)(x+3)(x²-3x+9)-(54+x³)`
`=(x+3)(x²-x.3+3²)-54-x³`
`=x³+3³-54-x³`
`=x³+27-54-x³`
`=(x³-x³)+(27-54)`
`=-27`