`14)a³-b³-3a+3b`
`=(a³-b³)-3(a-b)`
`=(a-b)(a²+ab+b²)-3(a-b)`
`=(a-b)(a²+ab+b²-3)`
`15)x³+3x²-3x-1`
`=(x³-1)+(3x²-3x)`
`=(x-1)(x²+x+1)+3x(x-1)`
`=(x-1)(x²+x+1+3x)`
`=(x-1)(x²+4x+1)`
`16)x³-3x²-3x+1`
`=(x³+1)-(3x²+3x)`
`=(x+1)(x²-x+1)-3x(x+1)`
`=(x+1)(x²-x+1-3x)`
`=(x+1)(x²-4x+1)`
`17)x³-4x²+4x-1`
`=(x³-1)-(4x²-4x)`
`=(x-1)(x²+x+1)-4x(x-1)`
`=(x-1)(x²+x+1-4x)`
`=(x-1)(x²-3x+1)`
`18)4a²b²-(a²+b²-1)²`
`=(2ab)²-(a²+b²-1)²`
`=(2ab+a²+b²-1)(2ab-a²-b²+1)`
`=[(a²+2ab+b²)-1][(1-(a²-2ab+b²)]`
`=[(a+b)²-1][(1-(a-b)²]`
`=(a+b+1)(a+b-1)(1+a-b)(1-a+b)`
`19)(xy+4)²-(2x+2y)²`
`=(xy+4+2x+2y)(xy+4-2x-2y)`
`=[(xy+2y)+(2x+4)][(xy-2y)-(2x-4)]`
`=[y(x+2)+2(x+2)][y(x-2)-2(x-2)]`
`=(x+2)(y+2)(x-2)(y-2)`
`20)(a²+b²+ab)²-a²b²-b²c²-c²a²`
`=[(a²+b²+ab)²-(ab)²]-(b²c²+c²a²)`
`=(a²+b²+ab+ab)(a²+b²+ab-ab)-c²(a²+b²)`
`=(a²+b²+2ab)(a²+b²)-c²(a²+b²)`
`=(a+b)²(a²+b²)-c²(a²+b²)`
`=(a²+b²)[(a+b)²-c²]`
`=(a²+b²)(a+b+c)(a+b-c)`
