`x^2+9-16y^2+6x`

`=(x^2+6x+9)-(4y)^2`

`=(x+3)^2-(4y)^2`

`=(x+3-4y)(x+3+4y)`

`x^2-9+y^2+2xy`

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

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

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

`x^2-4x+4-9y^2`

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

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

`x^2-4yx+4y^2-81`

`=(x-2y)^2-9^2`

`=(x-2y-9)(x-2y+9)`

`25-10x-9y^2+x^2`

`=(x^2-10x+25)-(3y)^2`

`=(x-5)^2-(3y)^2`

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

`9y^2-4x^2+4x-1`

`=9y^2-(4x^2-4x+1)`

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

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

`x^2-2x-4y^2+4y`

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

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

`64-4x^2+12xy-9y^2`

`=8^2-(4x^2-12xy+9y^2)`

`=8^2-(2x-3y)^2`

`=(8-2x+3y)(8+2x-3y)`