(x + 5)(x - 3) = ?

Options

A. `x^(2) + 5x - 15`
B. `x^(2) - 3x - 15`
C. `x^(2) + 2x + 15`
D. `x^(2) + 2x - 15`

Answer

To solve the expression \((x + 5)(x - 3)\), we will use the distributive property, also known as the FOIL method (First, Outside, Inside, Last). Here’s the step-by-step solution:

### Step 1: Apply the Distributive Property
We will multiply each term in the first bracket by each term in the second bracket.

\[ (x + 5)(x - 3) = x(x - 3) + 5(x - 3) \]

### Step 2: Multiply the First Term
Now, we will multiply \(x\) by both terms in the second bracket.

\[ x(x - 3) = x^2 - 3x \]

### Step 3: Multiply the Second Term
Next, we will multiply \(5\) by both terms in the second bracket.

\[ 5(x - 3) = 5x - 15 \]

### Step 4: Combine the Results
Now, we combine the results from Steps 2 and 3.

\[ x^2 - 3x + 5x - 15 \]

### Step 5: Combine Like Terms
Now, we will combine the like terms \(-3x\) and \(5x\).

\[ x^2 + (5x - 3x) - 15 = x^2 + 2x - 15 \]

### Final Answer
Thus, the expression \((x + 5)(x - 3)\) simplifies to:

\[ \boxed{x^2 + 2x - 15} \]

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