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

1 answer

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