1. What is the Difference of Squares?

The difference of squares is a binomial of the form x² - a² that can be factored into (x - a)(x + a). This is a fundamental algebraic identity used to simplify expressions and solve equations.

2. How Does the Calculator Work?

The calculator uses the difference of squares formula:

Where:

• \( x \) — Variable
• \( a \) — Any real number

Explanation: The formula shows that any binomial where one perfect square is subtracted from another can be factored into the product of two binomials.

3. Importance of Factoring

Details: Factoring is essential in algebra for simplifying expressions, solving equations, finding roots of polynomials, and analyzing mathematical models.

4. Using the Calculator

Tips: Simply enter the value of 'a' from your binomial expression x² - a². The calculator will return the factored form (x - a)(x + a).

5. Frequently Asked Questions (FAQ)

Q1: What if my expression isn't a difference of squares?
A: This calculator only works for x² - a² form. Other forms require different factoring methods.

Q2: Does this work for complex numbers?
A: Yes, the formula works for complex numbers, but this calculator currently handles real numbers only.

Q3: Can I factor x² + a² this way?
A: No, x² + a² cannot be factored using real numbers (it's a sum of squares, not difference).

Q4: What if 'a' is 0?
A: x² - 0² simplifies to just x², which is already in simplest form.

Q5: How is this used in solving equations?
A: Setting (x - a)(x + a) = 0 gives solutions x = a and x = -a (zero product property).