The difference of two squares

a²- b²= (a - b)(a + b)

Sometimes we have special cases of factoring, for example:

X²-1= (X -1)(X+1)
X²- 25 = (X-5)(X+5)

X²- 36 = (X-6)(X+6)

64X²-81Y²=(8X -9Y)(8X+9Y)


Binomials and Trinomials

When we have a binomial, we need to factor it by using these formulas

(a + b)² = a²+ 2ab + b²

(a - b)² = a²-2ab + b²


For example:

(3X + 9)² = (3X)²+ 2(3X)(9)+(9)²= 9X²- 54X + 81

(2X - 3Y)²= (2X)²- 2(2X)(3Y) +(3Y)²= 4X² -12XY + 9Y²


The Cube of a binomial

These are 

(a + b)³= a³+ 3a²b + 3ab²+ b³

(a -b)³= a³-3a²b + 3ab²-b³

For example:

(2X + 3)³ = (2X)³+3(2X)²(3) + 3(2X)(3)²+ (3)³ 
= 8X³+36X² + 54X + 27


(X - 4)³ = X³ -3(X)²4 + 3X(4)²- (4)³ = X³-12X²+ 48X - 64