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

Question

Responses

x2−2x+15
x squared minus 2 x plus 15

3x2−4x2−3x−15
3 x squared minus 4 x squared minus 3 x minus 15

x2−8x+15
x squared minus 8 x plus 15

2x−2

Answer 1

To verify which expression is equivalent to \((x−5)(x−3)\) using the Distributive Property (also known as FOIL in the case of binomials), we can multiply the two expressions:

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

Now let's simplify it step by step:

1. First: \(x \cdot x = x^2\)
2. Outer: \(x \cdot (-3) = -3x\)
3. Inner: \(-5 \cdot x = -5x\)
4. Last: \(-5 \cdot -3 = 15\)

Now, combine these results:

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

So, the equivalent expression is:

\[ \boxed{x^2 - 8x + 15} \]

Now, looking at the provided responses, the correct answer is:

x² − 8x + 15