This week we learned about the difference of squares and how when you have two of the same expression binomials except that one is negative and the other is positive the middle terms cancel each other out, leaving a subtraction of two terms squared (difference of squares).

A difference of squares if a factorization of (a – b)(a + b)

(a – b)(a + b) = a^2 + ab – ba – b^2

= a^2 – b^2

This works when factoring anything with the same terms but just different signs

Example

(3x – y)(3x + y)

 

9x^2 – y^2

Knowing this we can even work backwards

144p^2q^2 – 4

Knowing all the terms are squares we can start, first by removing the common factor if there is one.

4(36p^2q^2 – 1)

Now, we are still left with a difference of squares that we can factor.

4(6pq + 1)(6pq – 1)