1. **State the problem:** Factor the expression $$242f^2 - 32$$ completely. 2. **Identify the type of expression:** This is a difference of two terms, which can be factored using the difference of squares formula if possible. 3. **Factor out the greatest common factor (GCF):** The GCF of 242 and 32 is 2. $$242f^2 - 32 = 2(\cancel{121}f^2 - \cancel{16})$$ 4. **Recognize the difference of squares inside the parentheses:** $$121f^2 - 16 = (11f)^2 - 4^2$$ 5. **Apply the difference of squares formula:** $$a^2 - b^2 = (a - b)(a + b)$$ So, $$121f^2 - 16 = (11f - 4)(11f + 4)$$ 6. **Write the fully factored form:** $$242f^2 - 32 = 2(11f - 4)(11f + 4)$$ **Final answer:** $$2(11f - 4)(11f + 4)$$