1. **State the problem:** Factor the expression $$2x^2 - 72y^2$$. 2. **Identify the common factor:** Both terms have a common factor of 2. 3. **Factor out the common factor:** $$2x^2 - 72y^2 = 2(x^2 - 36y^2)$$ 4. **Recognize the difference of squares:** The expression inside the parentheses is a difference of squares since $$36y^2 = (6y)^2$$. 5. **Apply the difference of squares formula:** $$a^2 - b^2 = (a - b)(a + b)$$ 6. **Factor the expression:** $$x^2 - 36y^2 = (x - 6y)(x + 6y)$$ 7. **Write the fully factored form:** $$2(x - 6y)(x + 6y)$$ **Final answer:** $$2(x - 6y)(x + 6y)$$