Perfect Square Trinomial Calculator - Multi-Tools

Perfect Square Trinomial Calculator

Enter Trinomial:

x² + x +

Perfect Square Trinomial Patterns

A perfect square trinomial follows one of these patterns:

(ax + b)² = a²x² + 2abx + b²

(ax - b)² = a²x² - 2abx + b²

How to Identify Perfect Square Trinomials

Check if the first and last terms are perfect squares
Verify that the middle term is twice the product of the square roots
Determine if the sign of the middle term matches the pattern

Example Problems

Example 1: x² + 6x + 9

Step 1: Check if it's a perfect square

First term: x² is a perfect square
Last term: 9 is a perfect square (3²)
Middle term: 6x = 2 × x × 3

Step 2: Factor

x² + 6x + 9 = (x + 3)²

Example 2: 4x² - 12x + 9

Step 1: Check if it's a perfect square

First term: 4x² is a perfect square (2x)²
Last term: 9 is a perfect square (3²)
Middle term: -12x = 2 × 2x × (-3)

Step 2: Factor

4x² - 12x + 9 = (2x - 3)²

Common Patterns

Pattern	Example
(x + a)²	x² + 2ax + a²
(x - a)²	x² - 2ax + a²
(ax + b)²	a²x² + 2abx + b²

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