The second rule to factoring is to look for special products with two terms. A difference of two squares, a sum of two cubes, and a difference of two cubes are all factorable with special formulas.

Rule #2

If a polynomial has two terms, it's probably one of the special ones.
DOTS—Difference of Two Squares

a2 – b2 = (a – b)(a + b)		 Example: 4x2 – 9y4

= (2x - 3y)(2x + 3y)
DOTC—Difference of Two Cubes

a3 – b3 = (a – b)(a2 + ab + b2)		 Example: 27m3 – 1

= (3m)3 – 1

= (3m – 1)(9m2 + 3m + 1)
SOTC—Sum of Two Cubes

a3 + b3 = (a + b)(a2 – ab + b2)		 Example: 16w4 + w

= 2w(8w3 + 1) by Rule #1

= 2w(2w + 1)(4w2 – 2w + 1)

Did you notice that the Sum of Two Squares is not listed? A Sum of Two Squares is not factorable with the methods you are learning.

Use a separate sheet of paper to match these types of special polynomials with their examples.

1. x3 − 8y3 A. Difference of Two Squares
2. 16x2 + 25 B. Difference of Two Cubes
3. 4x2 − 49y2 C. Sum of Two Cubes
4. 64x3 + y3 D. Not Factorable

Factor the equations that are factorable. Write your answers in your notes.

Interactive popup. Assistance may be required.

Check Your Answer

All of these are perfect square trinomials.
  1. B (x – 2y)(x2 + 2xy + 4y2)
  2. D Not factorable
  3. A (2x – 7y)(2x + 7y)
  4. C (4x + y)(16x2 - 4xy + y2)
Close Pop Up

Do you need more help factoring cubes? Follow the link below to see a video explaining how to factor cubes.

Video segment. Assistance may be required. Factoring Cubes