`a^2 + 6ab +9b^2-1`

`= (a+3b)^2 -1^2`

`=(a+3b -1)(a+3b+1)`

`4x^2 -25 +(2x+7)(5-2x)`

`= (2x-5)(2x+5) - (2x+7)(2x-5)`

`=(2x-5)(2x+5-2x-7)`

`= -2(2x-5)`

`5(x+3y)-15x(x+3y)`

`= (x+3y)(5-15x)`

`= 5(x+3y)(1-3x)`

`x(x+y)^2 -y(x+y)^2 +xy-x^2`

`=x(x+y)^2 -y(x+y)^2 + x(y-x)`

`= (x+y)^2(x-y) -x(x-y)`

`= (x-y)(x^2+2xy+y^2 -x)`

`a^2-6a -b^2+9`

`= (a^2-6a+9)-b^2`

`=(a-3)^2-b^2`

`=(a-3-b)(a-3+b)`

`x^3-y^3 -3x^2+3x-1`

`=(x^3 -3x^2+3x-1)-y^3`

`=(x-1)^3 -y^3`

`=(x-1-y) [(x-1)^2 - y(x-1) + y^2]`

`= (x-1-y)( x^2-2x+1-xy+y+y^2)`