Difference of Squares Practice Test

About This Difference of Squares Practice Test

A difference of squares has the form A²-B² and factors as (A-B)(A+B). The pattern is most useful when both terms are perfect squares and subtraction separates them, but many problems require a greatest common factor or more than one factoring step first.

This test includes direct factorization, scaled and multivariable forms, quartic and sixth-degree expressions, complete factoring, equations, missing constants, real-number factorization, and short area or product applications.

Factoring Skills Covered

You will identify square terms, extract a GCF, write conjugate factors, factor repeatedly, solve zero-product equations, recognize sums that do not fit the pattern, and use known factors to recover missing values.

How to Approach the Questions

1. Factor out any common numerical or variable factor first.
2. Confirm that the remaining expression is subtraction of two exact squares.
3. Take the square root of each term and write conjugate factors.
4. Check whether either factor can be factored again, and verify by multiplication.

Common Mistakes to Avoid

Common mistakes include using the original terms instead of their square roots, writing two identical factors, applying the pattern to a sum of squares, stopping before complete factorization, forgetting a GCF, and keeping only one root when solving an equation.

Practice Format

Use this free 20-question test for Algebra 1, Algebra 2, factoring review, classroom practice, tutoring, or independent study.