Subtract :
`a^(2) + ab + b^(2)` from `4a^(2) - 3ab + 2b^(2)`

Answer

To solve the problem of subtracting \( a^2 + ab + b^2 \) from \( 4a^2 - 3ab + 2b^2 \), we will follow these steps:

### Step 1: Write the expression for subtraction
We need to subtract \( a^2 + ab + b^2 \) from \( 4a^2 - 3ab + 2b^2 \). This can be expressed as:
\[ (4a^2 - 3ab + 2b^2) - (a^2 + ab + b^2) \]

### Step 2: Distribute the negative sign
Next, we distribute the negative sign across the second expression:
\[ 4a^2 - 3ab + 2b^2 - a^2 - ab - b^2 \]

### Step 3: Combine like terms
Now, we will combine the like terms:
- For \( a^2 \) terms: \( 4a^2 - a^2 = 3a^2 \)
- For \( ab \) terms: \( -3ab - ab = -4ab \)
- For \( b^2 \) terms: \( 2b^2 - b^2 = 1b^2 \)

Putting it all together, we have:
\[ 3a^2 - 4ab + b^2 \]

### Final Answer
Thus, the result of subtracting \( a^2 + ab + b^2 \) from \( 4a^2 - 3ab + 2b^2 \) is:
\[ 3a^2 - 4ab + b^2 \]

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