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

To solve the equation \[ \frac{(3b)^2 + 12ab^5}{3b} = \square b + \square ab, \] we will simplify the left-hand side step by step. 1. **Calculate \((3b)^2\)**: \[ (3b)^2 = 9b^2. \] 2. **Substitute this back into the equation**: \[ \frac{9b^2 + 12ab^5}{3b}. \] 3. **Separate the terms in the numerator**: \[ \frac{9b^2}{3b} + \frac{12ab^5}{3b}. \] 4. **Simplify each term**: - For the first term: \[ \frac{9b^2}{3b} = 3b. \] - For the second term: \[ \frac{12ab^5}{3b} = 4ab^4. \] 5. **Combine the simplified terms**: \[ 3b + 4ab^4. \] Now we can rewrite the equation as: \[ 3b + 4ab^4 = \square b + \square ab. \] From this, we can identify the coefficients: - The coefficient of \(b\) is \(3\). - The coefficient of \(ab\) is \(4b^3\) (since \(4ab^4\) can be expressed as \(4a b^4\)). Thus, we can fill in the squares: \[ \boxed{3} b + \boxed{4} ab. \]