Special Products and Factoring

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