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

Question

.(1 point)
Responses

x2−2x+15
x squared minus 2 x plus 15

x2−8x+15
x squared minus 8 x plus 15

2x−2
2 x minus 2

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

Answer 1

To use the Distributive Property to verify the expression equivalent to \((x−5)(x−3)\), we can expand it:

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

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 all the terms:

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

So, \((x-5)(x-3) = x^2 - 8x + 15\).

Now, we can look at the given options:

1. \(x^2 - 2x + 15\) (not equivalent)
2. \(x^2 - 8x + 15\) (this is equivalent)
3. \(2x - 2\) (not equivalent)
4. \(3x^2 - 4x^2 - 3x - 15\) (not equivalent)

The correct expression equivalent to \((x−5)(x−3)\) is:

\(x^2 - 8x + 15\).