`17)(2x+1)²-(x-1)²`
`=[(2x+1)+(x-1)][(2x+1)-(x-1)]`
`=(2x+1+x-1)(2x+1-x+1)`
`=3x(x+2)`
`18)9(x+5)²-(x-7)²`
`=[3(x+5)]²-(x-7)²`
`=[3(x+5)+(x-7)][3(x+5)-(x-7)]`
`=(3x+15+x-7)(3x+15-x+7)`
`=(4x+8)(2x+22)`
`=4(x+2).2(x+11)`
`=8(x+2)(x+11)`
`19)25(x-y)²-16(x+y)²`
`=[5(x-y)]²-[4(x+y)]²`
`=[5(x-y)+4(x+y)][5(x-y)-4(x+y)]`
`=(5x-5y+4x+4y)(5x-5y-4x-4y)`
`=(9x-y)(x-9y)`
`20)49(y-4)²-9(y+2)²`
`=[7(y-4)]²-[3(y+2)]²`
`=[7(y-4)+3(y+2)][7(y-4)-3(y+2)]`
`=(7y-28+3y+6)(7y-28-3y-6)`
`=(10y-22)(4y-34)`
`=2(5y-11).2(2y-17)`
`=4(5y-11)(2y-17)`
`21)x^4+x^3+x+1`
`=(x^4+x^3)+(x+1)`
`=x^3(x+1)+(x+1)`
`=(x+1)(x^3+1)`
`=(x+1)(x+1)(x²-x+1)`
`=(x+1)^2(x²-x+1)`
`22)x^4-x^3-x^2+1`
`=(x^4-x^3)-(x^2-1)`
`=x^3(x-1)-(x+1)(x-1)`
`=(x-1)[x^3-(x+1)]`
`=(x-1)(x^3-x-1)`
`23)x²y+xy²-x-y`
`=(x²y+xy²)-(x+y)`
`=xy(x+y)-(x+y)`
`=(x+y)(xy-1)`
`24)a²x+a²y-7x-7y`
`=(a²x+a²y)-(7x+7y)`
`=a²(x+y)-7(x+y)`
`=(x+y)(a²-7)`
`=(x+y)[a^2-(`$\sqrt[]{7}$`)^2]`
`=(x+y)(a+`$\sqrt[]{7}$`)(a-`$\sqrt[]{7}$`)`
`25)ax²+ay-bx²-by`
`=(ax²-bx²)+(ay-by)`
`=x²(a-b)+y(a-b)`
`=(a-b)(x²+y)`
`26)x(x+1)²+x(x-5)-5(x+1)²`
`=[x(x+1)²-5(x+1)²]+x(x-5)`
`=(x+1)²(x-5)+x(x-5)`
`=(x-5)[(x+1)²+x]`
`=(x-5)(x²+2x+1+x)`
`=(x-5)(x²+3x+1)`
`27)3x²-12y²`
`=3(x²-4y²)`
`=3[x²-(2y)²]`
`=3(x+2y)(x-2y)`
`28)5xy²-10xyz+5xz²`
`=5x(y²-2yz+z²)`
`=5x(y-z)²`
`29)x³+3x²+3x+1-27z³`
`=(x³+3x²+3x+1)-27z³`
`=(x+1)³-(3z)³`
`=(x+1-3z)[(x+1)²+3z(x+1)+(3z)²]`
`=(x-3z+1)(x²+2x+1+3xz+3z+9z²)`
`30)x²-2xy+y²-xz+yz`
`=(x²-2xy+y²)-(xz-yz)`
`=(x-y)²-z(x-y)`
`=(x-y)(x-y-z)`
`31)x²-y²-x+y`
`=(x²-y²)-(x-y)`
`=(x+y)(x-y)-(x-y)`
`=(x-y)(x+y-1)`
`32)a³x-ab+b-x`
`=(a³x-x)-(ab-b)`
`=x(a³-1)-b(a-1)`
`=x(a-1)(a²+a+1)-b(a-1)`
`=(a-1)[x(a²+a+1)-b]`
`=(a-1)(a²x+ax+x-b)`
