To verify which expression is equivalent to \((x - 5)(x - 3)\) using the Distributive Property (also known as the FOIL method for binomials), we can expand the expression step by step.
-
Multiply the first terms: \(x \cdot x = x^2\)
-
Multiply the outer terms: \(x \cdot (-3) = -3x\)
-
Multiply the inner terms: \((-5) \cdot x = -5x\)
-
Multiply the last terms: \((-5) \cdot (-3) = 15\)
Now, combine all these results: \[ x^2 - 3x - 5x + 15 = x^2 - 8x + 15 \]
Thus, the fully expanded form of \((x - 5)(x - 3)\) is: \[ x^2 - 8x + 15 \]
Now, we need to compare this with the given options:
A) \(3x^2 - 4x^2 - 3x - 15\)
B) \(2x - 2\)
C) \(x^2 - 8x + 15\)
D) \(x^2 - 2x + 15\)
The expression that matches our expansion \(x^2 - 8x + 15\) is option C.
So, the answer is C \(x^2 - 8x + 15\).