4.6 Factoring a Difference of Squares
A difference of squares is a perfect square subtracted from a perfect square. Recall that a difference of squares can be written as factors containing the same terms but opposite signs because the middle terms cancel each other out when the two factors are multiplied.
[latex]a^2 - b^2 = (a+b)(a-b)[/latex]
We can use this equation to factor any differences of squares.
Difference of Squares
A difference of squares can be rewritten as two factors containing the same terms but opposite signs.
[latex]a^2 - b^2 = (a+b)(a-b)[/latex]
How To
Given a difference of squares, factor it into binomials.
- Confirm that the first and last term are perfect squares.
- Write the factored form as [latex](a+b)(a-b)[/latex].
Example 1: Factoring a Difference of Squares
- Factor [latex]9x^2 - 25[/latex].
- Factor [latex]81y^2-100[/latex].
Question & Answer
Is there a formula to factor the sum of squares?
No. A sum of squares cannot be factored.
Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites
