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Perfect Square Trinomial Calculator

Result

a²4
middle coefficient12
b²9
↗ Math

Perfect Square Trinomial Calculator — free online calculator.

Formula

For numeric a and b and the selected sign, (a + b)² = a² + 2ab + b² or (a − b)² = a² − 2ab + b². The tool returns the first coefficient a², the signed middle coefficient ±2ab, and the final term b²; it does not solve a general trinomial equation.
  • Perfect Square Trinomial Calculator calculates its result from a, b, Sign. It uses the formula Calculated with the verified ST Calculator runtime.. Change any input to recalculate the result instantly.
  • The main inputs are a, b, Sign. Enter them in the units and format shown in the calculator.
  • Keep comparable quantities in compatible units whenever the formula combines or compares them.
  • Changing any input above recalculates the result with the same calculation engine used by this page.

Example: Perfect Square Trinomial

Inputs
  • a: 2
  • b: 3
  • Sign: plus

Using a = 2, b = 3, Sign = plus, the calculated result is a²: 4 | middle coefficient: 12 | b²: 9.

Sample result: Calculating…

Frequently asked questions

What does the Perfect Square Trinomial calculate?

Perfect Square Trinomial Calculator — free online calculator.

Which values should I enter?

Enter a, b, Sign using the units and format shown beside each field.

What formula does this calculator use?

The calculator uses the following relationship: For numeric a and b and the selected sign, (a + b)² = a² + 2ab + b² or (a − b)² = a² − 2ab + b². The tool returns the first coefficient a², the signed middle coefficient ±2ab, and the final term b²; it does not solve a general trinomial equation..

Why might my result differ from another source?

Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.

Does the result update automatically?

Yes. Changing an input updates the result using the same calculation engine shown on this page.

Page information

Updated: October 7, 2026