Perfect Square Trinomial Calculator
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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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