1. **State the problem:** Factor the expression $9x^2 - 49y^2$. 2. **Formula used:** This is a difference of squares, which factors as $$a^2 - b^2 = (a - b)(a + b)$$ 3. **Identify squares:** Note that $9x^2 = (3x)^2$ and $49y^2 = (7y)^2$. 4. **Apply the formula:** Substitute $a = 3x$ and $b = 7y$ into the difference of squares formula: $$9x^2 - 49y^2 = (3x)^2 - (7y)^2 = (3x - 7y)(3x + 7y)$$ 5. **Final answer:** The factorization is $$(3x - 7y)(3x + 7y)$$