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

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UpStudy AI · Accepted Answer

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:
$$
\boxed{3} b + \boxed{4} ab.
$$
$$3b + 4ab$$.

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