Difference of Squares Identity Practice Test

About This Difference of Squares Identity Practice Test

The identity (A+B)(A-B)=A²-B² removes the middle terms of a conjugate product. It can simplify algebraic expressions and make products near a convenient base, such as 103·97 or 1001·999, much faster to calculate.

The questions use numbers, variables, radicals, nested binomials, given values of A+B and A-B, difference-of-square expressions, area models, and repeated conjugate products. The goal is flexible use of the identity rather than repeated basic factoring.

Identity Applications Covered

You will expand conjugates, compute products around a central value, simplify differences of two squares, recover a missing factor from a known product, combine the identity with sum-and-product information, and apply it to area differences.

How to Approach the Questions

1. Identify the common first quantity and the opposite second quantities.
2. Square each quantity and subtract the second square from the first.
3. For numerical products, choose the midpoint as the common base.
4. For nested expressions, treat each entire binomial as one quantity before simplifying.

Common Mistakes to Avoid

Typical errors include adding the squares, retaining a middle term, forgetting to square coefficients, choosing the wrong midpoint in mental multiplication, confusing a product of conjugates with a square of a binomial, and reversing the subtraction order.

Practice Format

Use this free 20-question test for algebraic identities, mental math, factoring support, classroom practice, or independent review.