📐 Perfect Square Trinomial Calculator
Factor perfect square trinomials
ax² + bx + c
How to Use This Calculator
Enter Coefficients
Type the coefficients a, b, and c of the trinomial ax² + bx + c.
Click Check
Determine if the trinomial is a perfect square.
See Result
See if it factors as (mx + n)² and the factored form.
Formula
Perfect Square: (mx + n)² = m²x² + 2mnx + n²
So we need: a = m², b = 2mn, c = n²
Example 1: x² + 6x + 9
m² = 1 → m = 1, n² = 9 → n = 3
Check: 2mn = 2(1)(3) = 6 ✓
Perfect square: (x + 3)²
Example 2: 4x² - 12x + 9
m² = 4 → m = 2, n² = 9 → n = 3
Check: 2mn = 2(2)(3) = 12, so b should be -12
Perfect square: (2x - 3)²
About Perfect Square Trinomial Calculator
The Perfect Square Trinomial Calculator checks if a trinomial is a perfect square and factors it. A perfect square trinomial is the result of squaring a binomial: (mx + n)² expands to m²x² + 2mnx + n².
When to Use This Calculator
- Factoring: Factor quadratics quickly
- Verification: Check if a trinomial is a perfect square
- Algebra: Simplify expressions
Pattern Recognition
- First and last terms must be perfect squares
- Middle coefficient must be 2√(first) × √(last)
- Sign of middle term determines binomial sign
Frequently Asked Questions
What makes a perfect square trinomial?
A trinomial of form a²x² + 2abx + b² where first and last terms are perfect squares and middle term is 2×√first×√last.
Can it have negative signs?
Yes! (mx - n)² = m²x² - 2mnx + n². The key is the ±2mn middle term.