What Is the Difference of Two Squares?
The difference of two squares is one of the most important algebraic identities. For any two numbers a and b, the expression a^2 - b^2 can always be factored into the product (a + b)(a - b). This calculator evaluates both the numeric result and shows the factored form, making it useful for checking homework, factoring polynomials, and mental-math shortcuts.
How to Use the Calculator
Enter your first value a and your second value b. The tool computes a^2, b^2, their difference, and the two factors (a + b) and (a - b). Values can be whole numbers, decimals, or negatives.
The Formula Explained
The identity comes from expanding the product:
The two middle terms cancel, leaving only a^2 - b^2. Because this works for every pair of numbers, it gives a quick way to factor any expression of the form (something)^2 - (something else)^2.
Worked Example
Let a = 7 and b = 3. Then a^2 = 49 and b^2 = 9, so a^2 - b^2 = 40. Using the factored form:
Both methods agree, confirming the identity.
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