(x^2-4)(x^2+6x+9) Factor

Jasonbradley

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Jun 17, 2024

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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.