Simplify:
`2x^(2)+3xy -3y^(2)+x^(2)-xy+y^(2)`

Answer

To simplify the expression \( 2x^2 + 3xy - 3y^2 + x^2 - xy + y^2 \), we will follow these steps:

### Step 1: Identify Like Terms
First, we need to identify the like terms in the expression. Like terms are terms that have the same variable raised to the same power.

- The terms with \( x^2 \) are \( 2x^2 \) and \( x^2 \).
- The terms with \( xy \) are \( 3xy \) and \( -xy \).
- The terms with \( y^2 \) are \( -3y^2 \) and \( y^2 \).

### Step 2: Group the Like Terms
Now, we will group the like terms together:

\[ (2x^2 + x^2) + (3xy - xy) + (-3y^2 + y^2) \]

### Step 3: Simplify Each Group
Next, we simplify each group of like terms:

1. For \( 2x^2 + x^2 \):
\[ 2x^2 + x^2 = 3x^2 \]

2. For \( 3xy - xy \):
\[ 3xy - xy = 2xy \]

3. For \( -3y^2 + y^2 \):
\[ -3y^2 + y^2 = -2y^2 \]

### Step 4: Combine the Results
Now, we combine the results from each group:

\[ 3x^2 + 2xy - 2y^2 \]

### Final Answer
Thus, the simplified expression is:

\[ \boxed{3x^2 + 2xy - 2y^2} \]

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