1. **State the problem:** We are given a function $f(x) = 2x + 5$ and an expression involving $f(x)$: $$f(x)f(x) - ff(x) = ax^2 + bx + c.$$ We need to find the values of $a$, $b$, and $c$. 2. **Understand the expression:** The expression $f(x)f(x) - ff(x)$ is interpreted as $f(x) \cdot f(x) - 2f(x) + 5$ based on the user's expansion. 3. **Calculate $f(x)f(x)$:** $$f(x)f(x) = (2x + 5)(2x + 5) = 4x^2 + 10x + 10x + 25 = 4x^2 + 20x + 25.$$ 4. **Calculate $-2f(x) + 5$:** $$-2f(x) + 5 = -2(2x + 5) + 5 = -4x - 10 + 5 = -4x - 5.$$ 5. **Combine the terms:** $$f(x)f(x) - 2f(x) + 5 = (4x^2 + 20x + 25) + (-4x - 5) = 4x^2 + (20x - 4x) + (25 - 5) = 4x^2 + 16x + 20.$$ 6. **Identify coefficients:** From the expression $$ax^2 + bx + c = 4x^2 + 16x + 20,$$ we see that: - $a = 4$ - $b = 16$ - $c = 20$ **Final answer:** $$a = 4, \quad b = 16, \quad c = 20.$$