Perfect Square Trinomial Calculator
Perfect Square Trinomial Calculator — expand (a±b)² or factor perfect square trinomials (a²±2ab+b²).
Formula
(a±b)² = a² ± 2ab + b²
- Perfect Square Trinomial: (a+b)² = a² + 2ab + b²
- Also: (a-b)² = a² - 2ab + b²
- Reverse (factoring): if trinomial = a² ± 2ab + b², then it factors as (a±b)²
Expand (3+4)²
Inputs
- Coefficient a: 3
- Coefficient b: 4
- Operation: plus
(3+4)² = 9 + 24 + 16 = 49. Verify: 7² = 49 ✓
Frequently asked questions
What is a perfect square trinomial?
A perfect square trinomial is a polynomial that factors into (a±b)². It has the form a² ± 2ab + b².
How do I factor a perfect square trinomial?
Check if it matches a² ± 2ab + b². If so, it factors as (a±b)². For example, x² + 6x + 9 = (x+3)².
Why is 2ab important?
The middle term 2ab (or -2ab) is the key to recognizing a perfect square trinomial. It's always twice the product of the square roots of the first and last terms.
Can I use this to solve quadratics?
Yes. Equations like (x+3)² = 0 solve quickly. Expand, set to 0, and solve x = -3.