Overview
The difference of squares is a well-known algebraic identity that links the difference of two squares to the product of their sum and difference. It simplifies large calculations without long multiplication and is widely used in factoring.
Formula
a² − b² = (a − b)(a + b).
How it works
Identify the two numbers
Write a and b so the expression is a² − b².
Compute difference and sum
Calculate a − b and a + b.
Multiply the factors
Multiply (a − b)(a + b) to get the value.
Verify
Compare the result with a² − b² directly.
Worked examples
Example 1: 5² − 3²
= (5 − 3)(5 + 3) = 2 × 8 = 16.
Example 2: 101² − 99²
= (101 − 99)(101 + 99) = 2 × 200 = 400.
Frequently asked questions
Does the identity work for negative numbers?
Yes. It is an algebraic identity valid for all real numbers.
What is the difference between difference and sum of squares?
A difference of squares factors into two factors, while a sum of squares usually does not factor over the reals.
Where is this identity used?
In simplifying expressions, solving equations and computing large differences quickly.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.