Multiply
`(7a^(2) b - 5ab^(2) +3ab) " by " (- 2ab) `

Answer

To solve the problem of multiplying the algebraic expression \( (7a^2b - 5ab^2 + 3ab) \) by \( -2ab \), we will follow these steps:

### Step 1: Write down the expression to be multiplied
We start with the expression:
\[ -2ab \times (7a^2b - 5ab^2 + 3ab) \]

### Step 2: Distribute \( -2ab \) to each term in the parentheses
We will distribute \( -2ab \) to each term inside the parentheses:
\[ -2ab \times 7a^2b + (-2ab) \times (-5ab^2) + (-2ab) \times 3ab \]

### Step 3: Multiply \( -2ab \) with the first term \( 7a^2b \)
Calculating the first term:
\[ -2ab \times 7a^2b = -14a^{2+1}b^{1+1} = -14a^3b^2 \]

### Step 4: Multiply \( -2ab \) with the second term \( -5ab^2 \)
Calculating the second term:
\[ -2ab \times (-5ab^2) = 10a^{1+1}b^{1+2} = 10a^2b^3 \]

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

### Step 6: Combine all the results
Now we combine all the results from the three multiplications:
\[ -14a^3b^2 + 10a^2b^3 - 6a^2b^2 \]

### Step 7: Rearrange and simplify if possible
We can rearrange the terms:
\[ -14a^3b^2 + (10a^2b^3 - 6a^2b^2) \]
Notice that \( 10a^2b^3 - 6a^2b^2 \) can be combined:
\[ = -14a^3b^2 + 4a^2b^2 \]

### Final Answer
Thus, the final result of the multiplication is:
\[ -14a^3b^2 + 4a^2b^2 \]