Question

Use the Distributive Property to verify which expression is equivalent to (x−5)(x−3).(1 point) RespoUse the Distributive Property to find which expression is equivalent to 9x2−25.(1 point) Responses (4.5x+12.5)(4.5x−12.5) left parenthesis 4.5 x plus 12.5 right parenthesis left parenthesis 4.5 x minus 12.5 right parenthesis 9x(x−25) 9 x left parenthesis x minus 25 right parenthesis (3x+5)(3x−5) left parenthesis 3 x plus 5 right parenthesis left parenthesis 3 x minus 5 right parenthesis (3x+5)2nses x2−8x+15 x squared minus 8 x plus 15 x2−2x+15 x squared minus 2 x plus 15 2x−2 2 x minus 2 3x2−4x2−3x−15

Answer 1

To find which expression is equivalent to (x−5)(x−3) using the Distributive Property (also known as the FOIL method for binomials):

1. **Distribute each term in the first binomial by each term in the second:**
\[
(x - 5)(x - 3) = x \cdot x + x \cdot (-3) + (-5) \cdot x + (-5) \cdot (-3)
\]
\[
= x^2 - 3x - 5x + 15
\]
\[
= x^2 - 8x + 15
\]

Now we can verify which expression is equivalent to \(9x^2 - 25\).

The expression \(9x^2 - 25\) is a difference of squares, which can be factored as:
\[
9x^2 - 25 = (3x)^2 - (5)^2 = (3x - 5)(3x + 5)
\]

Now, let's look at the options given:
- \((4.5x + 12.5)(4.5x - 12.5)\) - Incorrect
- \(9x(x - 25)\) - Incorrect
- \((3x + 5)(3x - 5)\) - **Correct**
- \((3x + 5)^2\) - Incorrect

So the equivalent expressions are:
1. For \((x−5)(x−3)\): **\(x^2 - 8x + 15\)**
2. For \(9x^2 - 25\): **\((3x + 5)(3x - 5)\)**.