## Factoring and Expanding (x+3)(x-3)(x+7)

This expression involves multiplying three binomials: (x+3), (x-3), and (x+7). We can solve it through two methods:

### 1. Expanding the expression

**Step 1:** Expand the first two binomials, (x+3) and (x-3).
This is a special case of the "difference of squares" pattern: (a+b)(a-b) = a² - b²

- (x+3)(x-3) = x² - 3² = x² - 9

**Step 2:** Multiply the result (x² - 9) by the remaining binomial (x+7)

- (x² - 9)(x + 7) = x²(x + 7) - 9(x + 7)
- = x³ + 7x² - 9x - 63

**Therefore, the expanded form of (x+3)(x-3)(x+7) is x³ + 7x² - 9x - 63**

### 2. Using the distributive property

**Step 1:** Multiply the first two binomials (x+3) and (x-3) using the distributive property.

- (x+3)(x-3) = x(x-3) + 3(x-3)
- = x² - 3x + 3x - 9
- = x² - 9

**Step 2:** Multiply the result (x² - 9) by the remaining binomial (x+7), again using the distributive property.

- (x² - 9)(x + 7) = x²(x + 7) - 9(x + 7)
- = x³ + 7x² - 9x - 63

**Therefore, the expanded form of (x+3)(x-3)(x+7) is x³ + 7x² - 9x - 63**

### Conclusion

Both methods, expanding and distributive property, lead to the same result: **x³ + 7x² - 9x - 63**. The choice of method depends on personal preference and the specific problem at hand.