When a = 2, b = -1, c = 0, find the value of expression `2a^(2)b + 2ab^(2) + 2abc`.

Answer

To find the value of the expression \(2a^2b + 2ab^2 + 2abc\) when \(a = 2\), \(b = -1\), and \(c = 0\), we will substitute the values of \(a\), \(b\), and \(c\) into the expression step by step.

### Step 1: Substitute the values into the expression
The expression is:
\[ 2a^2b + 2ab^2 + 2abc \]
Substituting \(a = 2\), \(b = -1\), and \(c = 0\):
\[ 2(2^2)(-1) + 2(2)(-1^2) + 2(2)(-1)(0) \]

### Step 2: Calculate each term
1. **First term**:
\[ 2(2^2)(-1) = 2(4)(-1) = 2 \times 4 \times -1 = -8 \]

2. **Second term**:
\[ 2(2)(-1^2) = 2(2)(1) = 2 \times 2 \times 1 = 4 \]

3. **Third term**:
\[ 2(2)(-1)(0) = 2 \times 2 \times -1 \times 0 = 0 \]

### Step 3: Combine the results
Now, we combine the results of all three terms:
\[ -8 + 4 + 0 \]

### Step 4: Simplify the expression
Calculating the above:
\[ -8 + 4 = -4 \]
Thus, the final result is:
\[ -4 \]

### Final Answer
The value of the expression \(2a^2b + 2ab^2 + 2abc\) when \(a = 2\), \(b = -1\), and \(c = 0\) is \(-4\).

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