Product of `6a^2 – 7b + 5ab and 2`ab is

Options

A. `12 a ^(2) b - 14 ab ^(2) + 10 ab `
B. `12 a ^(3) b - 14 ab ^(2) + 10 a ^(2) b ^(2)`
C. `6a ^(2) - 7b + 7ab`
D. `12 a ^(2) b - 7 ab ^(2) + 10 ab`

Answer

To find the product of the algebraic expression \(6a^2 - 7b + 5ab\) and \(2ab\), we will follow these steps:

### Step-by-Step Solution:

1. **Write the expression**:
We need to multiply the expression \(6a^2 - 7b + 5ab\) by \(2ab\).
\[ (6a^2 - 7b + 5ab) \cdot (2ab) \]

2. **Distribute \(2ab\) to each term**:
We will distribute \(2ab\) to each term in the expression \(6a^2 - 7b + 5ab\).
\[ = 6a^2 \cdot 2ab - 7b \cdot 2ab + 5ab \cdot 2ab \]

3. **Multiply each term**:
- For the first term:
\[ 6a^2 \cdot 2ab = 12a^3b \]
- For the second term:
\[ -7b \cdot 2ab = -14ab^2 \]
- For the third term:
\[ 5ab \cdot 2ab = 10a^2b^2 \]

4. **Combine the results**:
Now we combine all the terms we calculated:
\[ 12a^3b - 14ab^2 + 10a^2b^2 \]

5. **Final expression**:
The final expression after multiplying and combining like terms is:
\[ 12a^3b - 14ab^2 + 10a^2b^2 \]

### Final Answer:
\[ 12a^3b - 14ab^2 + 10a^2b^2 \]