Difference of Squares Calculator
Factor algebraic expressions using the difference of two squares formula. Step-by-step solver for polynomials and arithmetic.
Format not recognized. Please use difference of squares form (e.g., 25x^2 - 4).
About
In algebra, the "Difference of Squares" is a specific method used to factor polynomials. It applies when you have a binomial where one perfect square is subtracted from another. Recognizing this pattern allows students and engineers to simplify complex expressions rapidly. This tool serves a dual purpose: it acts as an instant solver for inputs like x2 - 16, and as an educational guide, breaking down the identification of terms a and b before applying the expansion formula.
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Formulas
The fundamental identity is:
a2 − b2 = (a − b)(a + b)
To use this, both terms must be perfect squares and they must be separated by a subtraction sign.
Reference Data
| Expression | Identify A | Identify B | Factored Form |
|---|---|---|---|
| x2 − 9 | x | 3 | (x-3)(x+3) |
| 4y2 − 25 | 2y | 5 | (2y-5)(2y+5) |
| 100 − a2 | 10 | a | (10-a)(10+a) |
| x4 − 1 | x2 | 1 | (x2-1)(x2+1) |
Frequently Asked Questions
No. The expression a^2 + b^2 cannot be factored using real numbers. It requires complex numbers (imaginary units), which this calculator does not currently support.
Example: 3x^2 - 12. You must first factor out the greatest common divisor (GCF). Factoring out 3 gives 3(x^2 - 4), which can then be solved as 3(x-2)(x+2).
Yes. The solver logic recognizes common variable characters (x, y, z, a, b) combined with standard power notation (^2).