====== Common Factorizations ======
Beyond simple distribution.
===== Difference of Squares =====
$(a^2 - b^2) = (a + b)(a - b)$
===== Sum of Squares =====
$(a^2 + b^2) = (a + bi)(a - bi)$
===== Sum/Difference of Cubes =====
$(a^3 + b^3) = (a + b)(a^2 - |ab| + b^2)$

$(a^3 - b^3) = (a - b)(a^2 + |ab| + b^2)$

An easy way to remember the difference is it goes sign -> same sign -> swap sign for quadratic.
===== Square of the Sum of Two Numbers =====
$(x + y)^2 = x^2 + 2xy + y^2$
===== Square of the Difference of Two Numbers =====
$(x - y)^2 = x^2 - 2xy + y^2$
===== Perfect Square Trinomial =====
$x^2 + bx + c = (x + \frac{b}{2})^2$ where $ \sqrt{c} = \frac{b}{2}$
===== Grouping =====
This one is a bit difficult to describe, so an example would do best.
  - $x^3 - 3x^2 - x + 3$ //example quadratic//
  - $x^3 - 3x^2$ **//__plus__//** $-x + 3$ //group terms with common factors//
  - $x^2(x - 3)$ **//__plus__//** $-1(x - 3)$ //reverse distribute common factors//
  - $(x^2 - 1)(x - 3)$ //reverse distribute the common group//((Remember that the equation really looks like $x^2(x - 3) + -1(x - 3)$, if you get confused by how there is a common factor between the groups))