Multiply `8a^(2)b - 3ab + 5b^(2)` by 6ab.

Answer

To solve the problem of multiplying the expression \(8a^2b - 3ab + 5b^2\) by \(6ab\), we will follow these steps:

### Step 1: Distribute \(6ab\) to each term in the expression
We will multiply \(6ab\) with each term in the expression \(8a^2b - 3ab + 5b^2\).

### Step 2: Multiply the first term
Multiply \(6ab\) with \(8a^2b\):
\[ 6ab \cdot 8a^2b = 48a^{2+1}b^{1+1} = 48a^3b^2 \]

### Step 3: Multiply the second term
Multiply \(6ab\) with \(-3ab\):
\[ 6ab \cdot (-3ab) = -18a^{1+1}b^{1+1} = -18a^2b^2 \]

### Step 4: Multiply the third term
Multiply \(6ab\) with \(5b^2\):
\[ 6ab \cdot 5b^2 = 30a^{1}b^{1+2} = 30ab^3 \]

### Step 5: Combine all the results
Now, we combine all the results from the previous steps:
\[ 48a^3b^2 - 18a^2b^2 + 30ab^3 \]

### Final Answer
The final result of multiplying \(8a^2b - 3ab + 5b^2\) by \(6ab\) is:
\[ 48a^3b^2 - 18a^2b^2 + 30ab^3 \]

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