Wxpanded and simplification of `(x +3) (x-1) ` will be equal to

Options

A. `x ^(2) + 2x -3`
B. `x ^(2) - 3x +2`
C. `x ^(2) - 2x + 3`
D. `x ^(2) + 3x - 3`

Answer

To expand and simplify the expression \((x + 3)(x - 1)\), we will follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ (x + 3)(x - 1) \]

### Step 2: Apply the distributive property (FOIL method)
We will use the FOIL method (First, Outside, Inside, Last) to expand the expression:
- **First**: Multiply the first terms: \(x \cdot x = x^2\)
- **Outside**: Multiply the outer terms: \(x \cdot (-1) = -x\)
- **Inside**: Multiply the inner terms: \(3 \cdot x = 3x\)
- **Last**: Multiply the last terms: \(3 \cdot (-1) = -3\)

Putting it all together, we have:
\[ x^2 - x + 3x - 3 \]

### Step 3: Combine like terms
Now, we combine the like terms:
- Combine \(-x\) and \(3x\):
\[ -x + 3x = 2x \]
So, the expression becomes:
\[ x^2 + 2x - 3 \]

### Final Result
Thus, the expanded and simplified form of \((x + 3)(x - 1)\) is:
\[ \boxed{x^2 + 2x - 3} \]

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