Expand the function. \( f(x)=(3 x-4)^{4} \) \( [?] x^{4}+\square x^{3}+\square x^{2}+\square x+\square \)

To expand the function \( f(x) = (3x - 4)^{4} \), we can use the binomial theorem, which states that \( (a + b)^{n} = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^{k} \). In this case, \( a = 3x \), \( b = -4 \), and \( n = 4 \). After applying the binomial theorem, we get: \( f(x) = \binom{4}{0} (3x)^{4} (-4)^{0} + \binom{4}{1} (3x)^{3} (-4)^{1} + \binom{4}{2} (3x)^{2} (-4)^{2} + \binom{4}{3} (3x)^{1} (-4)^{3} + \binom{4}{4} (3x)^{0} (-4)^{4} \). Calculating these terms: 1. \( 81x^{4} \) 2. \( -1080x^{3} \) 3. \( 720x^{2} \) 4. \( -1920x \) 5. \( 256 \) Putting it all together, we find: \( f(x) = 81x^{4} - 1080x^{3} + 720x^{2} - 1920x + 256 \). So, the expanded function is: \( 81x^{4} - 1080x^{3} + 720x^{2} - 1920x + 256 \).