Section 7.6: Special Factoring Cases
This section covers special factoring patterns: difference of squares, perfect square trinomials, and sum/difference of cubes.
Example 1: Difference of Squares
Factor: \( x^2 - 9 \)
Use \( a^2 - b^2 = (a - b)(a + b) \)
Here: \( x^2 - 3^2 = (x - 3)(x + 3) \)
Example 2: Perfect Square Trinomial
Factor: \( x^2 + 6x + 9 \)
Recognize \( a^2 + 2ab + b^2 = (a + b)^2 \)
Here: \( x^2 + 2*3*x + 3^2 = (x + 3)^2 \)
Example 3: Sum of Cubes
Factor: \( x^3 + 8 \)
Use \( a^3 + b^3 = (a + b)(a^2 - ab + b^2) \)
Here: \( x^3 + 2^3 = (x + 2)(x^2 - 2x + 4) \)
Practice Problems
- Factor: \( x^2 - 16 \)
- Factor: \( 9x^2 + 12x + 4 \)
- Factor: \( x^3 - 27 \)
- Factor: \( 4x^2 - 25 \)
- Factor: \( 8x^3 + 27 \)