Product of 6 ab, 3b and 4a is

Options

A. `72a ^(2) b ^(2)`
B. `144 ab `
C. `72ab`
D. `144 a^(2)b ^(2)`

Answer

To find the product of \(6ab\), \(3b\), and \(4a\), we can follow these steps:

### Step 1: Write down the expression
We start with the expression:
\[ 6ab \times 3b \times 4a \]

### Step 2: Group the coefficients and variables
We can separate the numerical coefficients and the variables:
\[ (6 \times 3 \times 4) \times (a \times b \times b \times a) \]

### Step 3: Calculate the numerical coefficients
Now, we calculate the product of the coefficients:
\[ 6 \times 3 = 18 \]
\[ 18 \times 4 = 72 \]

### Step 4: Combine the variables
Next, we combine the variables. We have:
\[ a \times a = a^2 \]
\[ b \times b = b^2 \]
Thus, the product of the variables is:
\[ a^2 \times b^2 \]

### Step 5: Combine the results
Now, we combine the results from the coefficients and the variables:
\[ 72 \times a^2 \times b^2 \]

### Final Answer
So, the final product is:
\[ 72a^2b^2 \]