Use the Distributive Property to verify which expression is equivalent to (x−5)(x−3).(1 point)

Question

Responses

3x^2−4x^2−3x−15
3 x squared minus 4 x squared minus 3 x minus 15
x^2−8x+15
x squared minus 8 x plus 15
x^2−2x+15
x squared minus 2 x plus 15
2x−2
2 x minus 2

Answer 1

To verify which expression is equivalent to \((x-5)(x-3)\) using the Distributive Property (also known as the FOIL method for binomials), we can expand the expression step by step.

1. Distribute the first terms: \[ x \cdot x = x^2 \]

2. Distribute the outer terms: \[ x \cdot (-3) = -3x \]

3. Distribute the inner terms: \[ -5 \cdot x = -5x \]

4. Distribute the last terms: \[ -5 \cdot (-3) = 15 \]

Now, we combine all these results:

\[ x^2 - 3x - 5x + 15 = x^2 - 8x + 15 \]

Thus, \((x-5)(x-3)\) simplifies to \(x^2 - 8x + 15\).

Among the provided responses:

• The expression that matches this result is: \[ x^2 - 8x + 15 \]
• The options are:
  • \(x^2 - 8x + 15\)
  • \(x^2 - 2x + 15\)
  • \(2x - 2\)

Therefore, the correct answer is \(x^2 - 8x + 15\).