The Special Forms are:
Perfect Square Trinomials
Difference of Two Squares
Sum of Cubes
Difference of Cubes
Perfect Square Trinomials: Factor the following expressions.
Recall: $(a+b)^2=a^2+2ab+b^2.$
That is, if the first and last terms of a trinomial are perfect squares, that's a hint that you might have a perfect square trinomial on your hands.
Example: $25r^2-60r+36$
A Difference of Two Squares
Recall: $(a+b)(a-b)=a^2-b^2.$
We use the above fact to factor expressions of the form $a^2-b^2$.
Examples
$x^2-4$
$36x^2-16$
$64s^2-y^2$
$w^2+49p^2$
Sums and Diferences of Cubes
Sum of Cubes: $a^3+b^3=(a+b)(a^2-ab+b^2)$
Difference of Cubes: $a^3-b^3=(a-b)(a^2+ab+b^2)$
Example: $27p^3+8$
Example: $64r^3-1$
Example: $27t^3+125u^3$