Difference of Squares

The Difference of Squares is a way of showing how an expression in the form \(x^2 - y^2\) can be written as the product of 2 binomials, with one as the Sum of Square Roots and the other as the Difference of Square Roots.

It can be expressed as:

\((x + y)(x - y)\)

Factoring Difference of Squares

  1. Determine if there is a Greatest Common Factor (GCF) that can be factored out of both terms. Include the GCF for the remainder of the expression
  2. Rewrite the expression in the form \((x)^2 - (y)^2\). Do this by finding the square root of both terms
  3. Use the formula \((a + b)(a – b)\) to factor the rest of the expression


Factor the binomial \(4x^2 - 25\)

We can rewrite the expression in the form \((x)^2 - (y)^2\):

\(= \sqrt{4x^2} - \sqrt{25}\)
\(= 2x - 5\)
\(= (2x)^2 - (5)^2\)

Use the formula \((x + y)(x - y)\) to factor the rest of the expression:

\(= (2x + 5)(2x - 5)\)

Therefore, we can determine that \(4x^2 - 25\) expressed as a Difference of Squares is \((2x + 5)(2x - 5)\).

Factor the following binomials:

\(121x^2 - 9y^2\)

\(18x^2 - 32\)

\((5c + 3)^2 - (2c + 1)^2\)

Find an algebraic expression for the area of the shaded region in factored form.