1)
\(x^2 - x - y^2 - y\)
\(= (x^2 - y^2) - (x + y)\)
\(= (x - y)(x + y) - (x + y)\)
\(= (x + y)(x - y - 1)\)

2)
\(x^2 - y^2 + x - y\)
\(= (x^2 - y^2) + (x - y)\)
\(= (x - y)(x + y) + (x - y)\)
\(= (x - y)(x + y + 1)\)

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

4)
\(5x - 5y + x^2 - y^2\)
\(= (5x - 5y) + (x^2 - y^2)\)
\(= 5(x - y) + (x - y)(x + y)\)
\(= (x - y)(5 + x + y)\)
\(= (x - y)(x + y + 5)\)

5)
\(x^2 - 5x - y^2 - 5y\)
\(= (x^2 - y^2) - (5x + 5y)\)
\(= (x - y)(x + y) - 5(x + y)\)
\(= (x + y)(x - y - 5)\)

6)
\(x^2 - y^2 + 2x - 2y\)
\(= (x^2 - y^2) + (2x - 2y)\)
\(= (x - y)(x + y) + 2(x - y)\)
\(= (x - y)(x + y + 2)\)

7)
\(x^2 - 4y^2 + x + 2y\)
\(= [x^2 - (2y)^2] + (x + 2y)\)
\(= (x - 2y)(x + 2y) + (x + 2y)\)
\(= (x + 2y)(x - 2y + 1)\)

8)
\(x^2 - y^2 - 2x - 2y\)
\(= (x^2 - y^2) - (2x + 2y)\)
\(= (x - y)(x + y) - 2(x + y)\)
\(= (x + y)(x - y - 2)\)

9)
\(x^2 - 4y^2 + 2x + 4y\)
\(= [x^2 - (2y)^2] + (2x + 4y)\)
\(= (x - 2y)(x + 2y) + 2(x + 2y)\)
\(= (x + 2y)(x - 2y + 2)\)

10)
\(x(x - y) + x^2 - y^2\)
\(= x(x - y) + (x - y)(x + y)\)
\(= (x - y)[x + (x + y)]\)
\(= (x - y)(x + x + y)\)
\(= (x - y)(2x + y)\)

11)
\(x^2 - y^2 + 10x - 10y\)
\(= (x^2 - y^2) + (10x - 10y)\)
\(= (x - y)(x + y) + 10(x - y)\)
\(= (x - y)(x + y + 10)\)

12)
\(x^2 - y^2 + 20x + 20y\)
\(= (x^2 - y^2) + (20x + 20y)\)
\(= (x - y)(x + y) + 20(x + y)\)
\(= (x + y)(x - y + 20)\)