Find `2x(x-3y)+2y^2` when x=-6 and y=3

Options

A. -9
B. 54
C. 81
D. 198

Answer

To solve the expression \(2x(x - 3y) + 2y^2\) when \(x = -6\) and \(y = 3\), we will follow these steps:

### Step 1: Substitute the values of \(x\) and \(y\)
We start by substituting \(x = -6\) and \(y = 3\) into the expression:
\[ 2(-6)((-6) - 3(3)) + 2(3^2) \]

### Step 2: Simplify inside the parentheses
Now, we simplify the expression inside the parentheses:
\[ -6 - 3(3) = -6 - 9 = -15 \]
So, the expression becomes:
\[ 2(-6)(-15) + 2(3^2) \]

### Step 3: Calculate \(3^2\)
Next, we calculate \(3^2\):
\[ 3^2 = 9 \]
Now, substitute this back into the expression:
\[ 2(-6)(-15) + 2(9) \]

### Step 4: Calculate \(2(-6)(-15)\)
Now, we calculate \(2(-6)(-15)\):
\[ 2(-6)(-15) = 2 \times 6 \times 15 = 180 \]
So, the expression now is:
\[ 180 + 2(9) \]

### Step 5: Calculate \(2(9)\)
Next, we calculate \(2(9)\):
\[ 2(9) = 18 \]
Now, we substitute this back into the expression:
\[ 180 + 18 \]

### Step 6: Add the results
Finally, we add the two results together:
\[ 180 + 18 = 198 \]

### Final Answer
Thus, the value of the expression \(2x(x - 3y) + 2y^2\) when \(x = -6\) and \(y = 3\) is:
\[ \boxed{198} \]