1. What is the Expanded Form?

The expanded form of a quadratic expression transforms \( a(x + b)^2 \) into its standard polynomial form \( a x^2 + 2 a b x + a b^2 \). This form is useful for analyzing polynomial behavior and solving equations.

2. How Does the Calculator Work?

The calculator uses the expanded form equation:

Where:

• \( a \) — Coefficient of the quadratic term
• \( b \) — Constant term inside the parentheses
• \( x \) — Variable

Explanation: The equation demonstrates how to expand a squared binomial expression into its polynomial components.

3. Importance of Expanded Form

Details: The expanded form is essential for polynomial analysis, finding roots, graphing parabolas, and solving quadratic equations. It reveals the coefficients needed for various algebraic operations.

4. Using the Calculator

Tips: Enter the coefficient (a) and constant (b) values. The calculator will show the expanded polynomial form. All values must be valid numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if coefficient (a) is zero?
A: The expression becomes linear, not quadratic. The calculator requires a non-zero coefficient.

Q2: How is this different from completing the square?
A: This is the reverse process - we're expanding rather than factoring.

Q3: Can this handle negative values?
A: Yes, the calculator works with both positive and negative values for a and b.

Q4: What's the degree of the expanded polynomial?
A: The expanded form is always a quadratic (degree 2) polynomial when a ≠ 0.

Q5: Can this be used for other polynomial expansions?
A: This specific calculator handles squared binomials. Other expansions would require different formulas.