Find the value of expression `6x^(3)(2x^(2)-1)` at x= 2.

Answer

To find the value of the expression \( 6x^3(2x^2 - 1) \) at \( x = 2 \), we will follow these steps:

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

### Step 2: Calculate \( 2^3 \)
Next, we calculate \( 2^3 \):
\[ 2^3 = 8 \]
So, our expression now looks like:
\[ 6 \cdot 8 \cdot (2(2^2) - 1) \]

### Step 3: Calculate \( 2^2 \)
Now, we calculate \( 2^2 \):
\[ 2^2 = 4 \]
Substituting this back into the expression gives us:
\[ 6 \cdot 8 \cdot (2 \cdot 4 - 1) \]

### Step 4: Calculate \( 2 \cdot 4 \)
Next, we calculate \( 2 \cdot 4 \):
\[ 2 \cdot 4 = 8 \]
Now our expression is:
\[ 6 \cdot 8 \cdot (8 - 1) \]

### Step 5: Simplify the expression inside the parentheses
Now we simplify \( (8 - 1) \):
\[ 8 - 1 = 7 \]
So, we have:
\[ 6 \cdot 8 \cdot 7 \]

### Step 6: Calculate \( 6 \cdot 8 \)
Next, we calculate \( 6 \cdot 8 \):
\[ 6 \cdot 8 = 48 \]
Now our expression is:
\[ 48 \cdot 7 \]

### Step 7: Calculate \( 48 \cdot 7 \)
Finally, we calculate \( 48 \cdot 7 \):
\[ 48 \cdot 7 = 336 \]

### Final Answer
Thus, the value of the expression \( 6x^3(2x^2 - 1) \) at \( x = 2 \) is:
\[ \boxed{336} \]