`1)4x^2-25+(2x+7)(5-2x)`
`=(2x)^2-5^2-(2x+7)(2x-5)`
`=(2x-5)(2x+5)-(2x+7)(2x-5)`
`=(2x-5)(2x+5-2x-7)`
`=-2(2x-5)`
`2)5x^2-5y^2-10x+10y`
`=(5x^2-5y^2)-(10x-10y)`
`=5(x^2-y^2)-10(x-y)`
`=5(x-y)(x+y)-10(x-y)`
`=5(x-y)(x+y-2)`
`3)ax-bx-a^2+2ab-b^2`
`=(ax-bx)-(a^2-2ab+b^2)`
`=x(a-b)-(a-b)^2`
`=(a-b)(x-a+b)`
`4)x^2+4x-y^2+4`
`=(x^2+4x+4)-y^2`
`=(x^2+2.x.2+2^2)-y^2`
`=(x+2)^2-y^2`
`=(x+2-y)(x+2+y)`
`5)x^3-x^2-x+1`
`=(x^3-x^2)-(x-1)`
`=x(x^2-1)-(x-1)`
`=x(x-1)(x+1)-(x-1)`
`=(x-1)(x^2+x-1)`
`6)2x^2-18`
`=2(x^2-9)`
`=2(x-3)(x+3)`
`7)x^2-7xy+10y^2`
`=x^2-5xy-2xy+10y^2`
`=(x^2-5xy)-(2xy-10y^2)`
`=x(x-5y)-2y(x-5y)`
`=(x-2y)(x-5y)`
`8)x^3-2x^2+x-xy^2`
`=x(x^2-2x+1-y^2)`
`=x[(x-1)^2-y^2]`
`=x(x-y-1)(x+y-1)`
`9)2xy-x^2-y^2+16`
`=-(x^2-2xy+y^2-16)`
`=-[(x-y)^2-4^2]`
`=-(x-y-4)(x-y+4)`
`10)x^3-x^2-6x`
`=x(x^2-x-6)`
`=x(x^2-3x+2x-6)`
`=x[(x^2-3x)+(2x-6)]`
`=x[x(x-3)+2(x-3)]`
`=x(x+2)(x-3)`
`11)x^2-2xy+y^2-z^2+2zt-t^2`
`=(x^2-2xy+y^2)-(z^2-2zt+t^2)`
`=(x-y)^2-(z-t)^2`
`=(x-y-z+t)(x-y+z-t)`
