Multiply :
`5x^(2) - 8xy + 6y^(2) - 3` by `-3xy`

Answer

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

### Step 1: Distribute \(-3xy\) to each term in the expression
We will multiply \(-3xy\) with each term of the expression \(5x^2 - 8xy + 6y^2 - 3\).

### Step 2: Multiply the first term
Multiply \(-3xy\) by \(5x^2\):
\[ -3xy \cdot 5x^2 = -15x^{2+1}y = -15x^3y \]

### Step 3: Multiply the second term
Multiply \(-3xy\) by \(-8xy\):
\[ -3xy \cdot (-8xy) = 24x^{1+1}y^{1+1} = 24x^2y^2 \]

### Step 4: Multiply the third term
Multiply \(-3xy\) by \(6y^2\):
\[ -3xy \cdot 6y^2 = -18xy^{1+2} = -18xy^3 \]

### Step 5: Multiply the fourth term
Multiply \(-3xy\) by \(-3\):
\[ -3xy \cdot (-3) = 9xy \]

### Step 6: Combine all the results
Now we combine all the terms we obtained from the multiplication:
\[ -15x^3y + 24x^2y^2 - 18xy^3 + 9xy \]

### Final Answer
Thus, the final expression after multiplying is:
\[ -15x^3y + 24x^2y^2 - 18xy^3 + 9xy \]

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