(x%5E2%2B6x%2B9)-factor.jpeg "(x^2-4)(x^2+6x+9) Factor")
Factoring the Expression (x² - 4)(x² + 6x + 9)
This expression involves factoring a product of two binomials. Let's break down the steps:
Step 1: Recognizing Patterns
- (x² - 4): This is a difference of squares pattern, where a² - b² = (a + b)(a - b). In this case, a = x and b = 2.
- (x² + 6x + 9): This is a perfect square trinomial pattern, where a² + 2ab + b² = (a + b)². In this case, a = x and b = 3.
Step 2: Applying the Patterns
- (x² - 4): Factoring this gives us (x + 2)(x - 2).
- (x² + 6x + 9): Factoring this gives us (x + 3)².
Step 3: Combining the Factors
Now we have: (x + 2)(x - 2)(x + 3)²
Final Factored Expression
Therefore, the completely factored expression of (x² - 4)(x² + 6x + 9) is (x + 2)(x - 2)(x + 3)².