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

Question

Responses

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
2 x minus 2

x2−2x+15

Answer 1

To verify which expression is equivalent to \((x−5)(x−3)\) using the Distributive Property, we will expand it.

Using the distributive property (often called FOIL for binomials):

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

Calculating each term:

1. \(x \cdot x = x^2\)
2. \(x \cdot (-3) = -3x\)
3. \((-5) \cdot x = -5x\)
4. \((-5) \cdot (-3) = 15\)

Now, combine these results:

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

So, the expanded form of \((x − 5)(x − 3)\) is:

\[ x^2 - 8x + 15 \]

Thus, the expression that is equivalent to \((x−5)(x−3)\) is:

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