**Special Products**

1. $(x + y)(x - y) = x^2 - y^2$

2. $(x + y)^2 = x^2 + 2xy + y^2$

3. $(x - y)^2 = x^2 - 2xy + y^2$

4. $(x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3$

5. $(x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3$

6. $(x + a)(x + b) = x^2 + (a + b)x + ab$

7. $(ax + by)(cx + dy) = acx^2 + (ad + bc)xy + bdy^2$

**Factoring Polynomials**

1. $ax + ay + az = a(x + y + z)$

2. $x^2 - y^2 = (x + y)(x - y)$

3. $x^3 + y^3 = (x + y)(x^2 - xy + y^2)$

4. $x^3 - y^3 = (x - y)(x^2 + xy + y^2)$

5. $x^2 + 2xy + y^2 = (x + y)^2$

6. $x^2 - 2xy + y^2 = (x - y)^2$

7. $x^2 + (a + b)x + ab = (x + a)(x + b)$

8. $acx^2 + (ad + bc)xy + bdy^2 = (ax + by)(cx + dy)$