Question

use the distributive property to verify which expression is equivalent to (x-5) (x-3)

Answer 1

To verify which expression is equivalent to \((x - 5)(x - 3)\) using the distributive property, we can expand the expression:

1. Apply the distributive property (also known as the FOIL method for binomials):
\[
(x - 5)(x - 3) = x \cdot x + x \cdot (-3) - 5 \cdot x - 5 \cdot (-3)
\]

2. Perform the multiplications:
\[
= x^2 - 3x - 5x + 15
\]

3. Combine like terms:
\[
= x^2 - 8x + 15
\]

Thus, the expression equivalent to \((x - 5)(x - 3)\) after using the distributive property is:
\[
x^2 - 8x + 15
\]

If you have specific expressions to compare against, you can check if any of them match \(x^2 - 8x + 15\).