TWO TERMS
TO BE FACTORABLE AN EXPRESSION WITH TWO TERMS MUST BE ONE OF THE FOLLOWING: If an expression fits both difference of two squares and difference of two cubes, first factor as the difference of two cubes. Some of the factors will be factorable now as the difference of two squares.
DIFFERENCE OF SQUARES
Recognizing terms that are perfect squares
Numbers: The square root of the number must be rational. The square root will be a whole number, a fraction,or a decimal that is repeating or terminating.
Letters with exponents: The exponent of the letter must be even.
Letters and numbers: Both must be perfect squares.

64 is a perfect square since its square root is 8.
1/4 is a perfect square since its square root is 1/2.
x8 is a perfect square since 8 is even.
x9 is not a perfect square since 9 is not even.
9x4 is a perfect square. (It's square root is 3x2)
3x2 is not a perfect square since 3 is not a perfect square.

Factoring the difference of two squares
If an expression is of the form perfect square - perfect square it will factor into two binomials that have the same terms but opposite signs between them.
To factor A2 - B2 the two binomials would be (A - B)(A + B)
The pattern will be the same for any perfect square minus perect square with the first positions being the square root of the first term and the second positions being the square root of the second term.
To factor 4x2 - 9y2 we will get (2x - 3y)(2x + 3y)
 
 
 SUMS AND DIFFERENCES OF CUBES
Recognizing terms that are perfect cubes
Numbers: The cube root of numbers must be rational. It can be a whole number, a fraction or a terminating or repeating decimal.
Letters with exponents: All letters must have powers that are divisible by three.
Letters and numbers:  All factors must  be perfect cubes.
64 is a perfect cube since its cube root is 8.
1/8 is a perfect square since its square root is 1/2.
x8 is not a perfect cube since 8 is not divisible by 3.
x9 is  a perfect cube since 9 is divisible by 3.
27x6 is a perfect cube. (Its cube root is 3x2)
3x6 is not a perfect cube since 3 is not a perfect cube.
Factoring sums or differences of Cubes

First we label an A and a B: A= cube root of the first term
                                            B= cube root of the second term
Choose the appropriate formula (depending on whether the expression you are factoring is a sum or a difference.) Replace the letter A with its equivalent and the letter B with its equivalent. Simplify.

(A3 + B3) = (A + B)(A2 - AB + B2)
(A3 - B3) = (A - B)(A2 + AB + B2)