Algebra 101 - Unit 5

Lesson 31: Factoring Special Cases (Difference of Squares, Perfect Square Trinomial)

Some polynomials follow special factoring patterns that can save time and effort. The most common special cases are difference of squares and perfect square trinomials.

Difference of Squares

Pattern: a² − b² = (a + b)(a − b)

Examples:

• x² − 9 = (x + 3)(x − 3)
• 4x² − 25 = (2x + 5)(2x − 5)
• 9x⁴ − 16y² = (3x² + 4y)(3x² − 4y)

Perfect Square Trinomial

Pattern: a² + 2ab + b² = (a + b)² or a² − 2ab + b² = (a − b)²

Examples:

• x² + 6x + 9 = (x + 3)²
• 4x² − 12x + 9 = (2x − 3)²
• x² + 10x + 25 = (x + 5)²

Practice Problems

1. Factor x² − 16
2. Factor 9x² − 49
3. Factor x² + 8x + 16
4. Factor 4x² − 12x + 9
5. Factor 25x² − 36y²