Square of a Binomial Calculator
Expand the square of any binomial expression of the form (ax + b)² or (ax - b)² into standard quadratic trinomial form a²x² ± 2abx + b².
Enter Calculation Inputs
Fill in the fields below. Instant client-side computation runs automatically in your browser as you type.
Common Searches & Natural Queries
What is the Square of Binomial?
The square of a binomial is a special algebraic product yielding a perfect square trinomial. Rather than performing manual polynomial multiplication (FOIL), the rule dictates that the square of (a + b) equals the square of the first term, plus twice the product of both terms, plus the square of the second term.
Mathematical Formula & Methodology
The mathematical model underlying this tool operates on the following verified equation:
(ax + b)² = a²x² + 2abx + b² | (ax - b)² = a²x² - 2abx + b²
Understanding the Parameters:
- Coefficient a — Primary input variable.
- Sign (+ or -) — Primary input variable.
- Term b — Primary input variable.
How to Use This Calculator
Specify the coefficient for x, the operation (+ or -), and the second constant or term. Click Calculate to see the complete expansion along with intermediate terms.
Worked Numerical Example
Expand (2x + 3)²: First term squared: (2x)² = 4x². Twice product: 2 × (2x) × (3) = 12x. Last term squared: 3² = 9. Expanded trinomial: 4x² + 12x + 9.
Key Considerations & Standards
The middle term sign matches the binomial sign (+ for addition, - for subtraction), while the last term (b²) is always non-negative for real numbers.
Frequently Asked Questions
Why is the last term always positive in (a - b)²?
Because squaring any real negative number yields a positive product: (-b) × (-b) = +b².
What is the FOIL method?
FOIL stands for First, Outer, Inner, Last—the sequence for multiplying two binomials. The binomial square formula is the algebraic shortcut for FOIL when both factors are identical.