Lesson 27: Special Products (Squares, Difference of Squares)
Certain polynomial products have special patterns that make multiplication easier. The most common are perfect square trinomials and difference of squares.
Perfect Square Trinomials
When a binomial is squared, the result follows this pattern:
(a + b)² = a² + 2ab + b²
(a − b)² = a² − 2ab + b²
Example 1:
(x + 5)² = x² + 2(x)(5) + 5² = x² + 10x + 25
Example 2:
(3x − 2)² = (3x)² − 2(3x)(2) + 2² = 9x² − 12x + 4
Difference of Squares
The difference of squares pattern is:
a² − b² = (a + b)(a − b)
Example 1:
x² − 16 = (x + 4)(x − 4)
Example 2:
9x² − 25 = (3x + 5)(3x − 5)
Practice Problems
- Expand (x + 7)²
- Expand (2x − 3)²
- Factor x² − 49
- Factor 16x² − 25
- Expand (x − 4)²