\( \frac { ( 3 b ) ^ { 2 } + 12 a b ^ { 5 } } { 3 b } = \square b + \square a b \)

We start with the given expression: \[ \frac{(3b)^2 + 12ab^5}{3b}. \] 1. First, expand \((3b)^2\): \[ (3b)^2 = 9b^2. \] So the numerator becomes: \[ 9b^2 + 12ab^5. \] 2. Write the expression as two separate fractions: \[ \frac{9b^2}{3b} + \frac{12ab^5}{3b}. \] 3. Simplify each term individually: - For the first term: \[ \frac{9b^2}{3b} = \frac{9}{3} \cdot \frac{b^2}{b} = 3b. \] - For the second term: \[ \frac{12ab^5}{3b} = \frac{12}{3} \cdot a \cdot \frac{b^5}{b} = 4a b^{5-1} = 4ab^4. \] 4. Combine the simplified terms: \[ 3b + 4ab^4. \] Thus, the expression simplifies to: \[ \frac{(3b)^2 + 12ab^5}{3b} = 3b + 4ab^4. \] If the blanks are intended for the coefficients of each term, then they are \(3\) in the first term and \(4\) in the second term (noting that the second term is actually \(4ab^4\) rather than \(4ab\)).