Perfect Square Trinomial Calculator

Check or create perfect square trinomials

Coefficient a (x²)

Coefficient b (x)

Constant c

Positive Pattern

(a + b)² = a² + 2ab + b²

Square of a sum

Negative Pattern

(a - b)² = a² - 2ab + b²

Square of a difference

Recognition Rule

b² = 4ac

Middle term squared = 4 × first × last

General Form

ax² ± 2√(ac)x + c

Perfect square structure

x² + 6x + 9

= (x + 3)²

Perfect square ✓

x² - 10x + 25

= (x - 5)²

Perfect square ✓

4x² + 12x + 9

= (2x + 3)²

Perfect square ✓

9x² - 30x + 25

= (3x - 5)²

Perfect square ✓

Algebra

• Factoring trinomials

• Completing the square

• Solving equations

Geometry

• Area calculations

• Square dimensions

• Pythagorean theorem

Calculus

• Integration

• Optimization

• Curve analysis