Algebra Homework Help : Factorization - Difference of Two Squares

How to factor a difference of two squares ?

The difference of two squares is commonly encountered in algebra and can be factored as follows :

a² − b² = (a + b)(a − b)

This is easily verified by expansion as shown below.
(a + b)(a − b) = a(a − b) + b(a − b) = a² − ab + ba − b² = a² − b²

Thus, the difference of two squares is a binomial expression where the two terms are perfect squares with one term positive and the other negative.

Example : 32x² − 18 = 2(16x² − 9) = 2(4x + 3)(4x − 3)
In the above example, first 2 is factored out. Then what's left is the difference of two squares, which can be factored further. The square root of the first term (16x²) is 4x while the square root of the second term (9) is 3.

 Practice Exercise for Algebra Module on Difference of Two Squares