x² − 49
Show answer
(x − 7)(x + 7)
Free printable worksheet
Difference of Squares Worksheet
Twenty expressions emphasizing perfect-square recognition and complete factorization.
Algebra 1Grades 7-103 pagesAnswer key included
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Download the free PDF
What this worksheet includes
- Twenty expressions emphasizing perfect-square recognition and complete factorization.
- 3-page printable PDF with a complete answer key
- Designed for Grades 7-10 algebra 1 practice
- Available as an immediate free download with no email required
How to use it
Use this difference of squares worksheet for guided practice, independent review, homework, tutoring sessions, or a quick skills check. The spacious layout is designed to leave room for students to show their work rather than guess from crowded answer choices.
After students finish, compare their reasoning with the included answer key. When an answer is incorrect, have the student locate the first step where their work changed direction before trying the problem again.
Who this practice is for
This resource is designed for grades 7-10 students working on algebra 1. Teachers, tutors, homeschool families, and parents can preview the first page before deciding whether the level and spacing fit the student.
Looking for a broader sequence? Browse all Algebra I worksheets.
Topic guide
How to approach difference of squares
A difference of squares has the form a² − b² and factors as (a − b)(a + b). Both terms must be perfect squares and the operation between them must be subtraction.
Expressions may need a greatest common factor removed first, and powers such as x⁴ should be viewed as (x²)². Continue factoring until neither factor contains another difference of squares.
Learning objectives
- Recognize perfect-square terms
- Apply a² − b² = (a − b)(a + b)
- Factor expressions completely
Skills to review first
- Perfect squares
- Exponent notation
- Greatest common factors
Worked example
Follow the reasoning step by step
Factor 9x² − 25.
- Recognize 9x² = (3x)².
- Recognize 25 = 5².
- Apply the difference-of-squares pattern.
- Check (3x − 5)(3x + 5) by multiplication.
Solution: (3x − 5)(3x + 5).
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
16a² − 81
Show answer
(4a − 9)(4a + 9)
25m⁴ − 4n²
Show answer
(5m² − 2n)(5m² + 2n)
Error check
Common mistakes to watch for
- Applying the pattern to a sum of squares
- Taking an incorrect square root of a variable power
- Leaving a factor that can be factored again