To verify which expression is equivalent to \((x - 5)(x - 3)\) using the distributive property, we can expand the expression:
-
Apply the distributive property (also known as the FOIL method for binomials): \[ (x - 5)(x - 3) = x \cdot x + x \cdot (-3) - 5 \cdot x - 5 \cdot (-3) \]
-
Perform the multiplications: \[ = x^2 - 3x - 5x + 15 \]
-
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 \(x^2 - 8x + 15\).