se the Distributive Property to verify which expression is equivalent to (x−5)(x−3).
To verify which expression is equivalent to (x-5)(x-3) using the Distributive Property, we need to multiply both terms of the second factor (x-3) by the first term (x) in the first factor and the second term (-5) in the first factor separately.
Using the Distributive Property, we get:
(x-5)(x-3) = x(x-3) - 5(x-3)
Expanding the expression further:
= x(x) - x(3) - 5(x) + 5(3)
Multiplying:
= x^2 - 3x - 5x + 15
Combining like terms:
= x^2 - 8x + 15
Therefore, the expression (x^2 - 8x + 15) is equivalent to (x - 5)(x - 3) using the Distributive Property.
To verify the equivalent expression using the Distributive Property, we need to expand the given expression (x-5)(x-3) and simplify.
Step 1: Distribute the first term (x) to both terms in the second parentheses, which is (x-3):
x(x-3) - 5(x-3)
Step 2: Apply the Distributive Property:
x*x - x*3 - 5*x + 5*3
Step 3: Simplify each term:
x^2 - 3x - 5x + 15
Step 4: Combine like terms:
x^2 - 8x + 15
Therefore, the expression (x-5)(x-3) is equivalent to x^2 - 8x + 15 after applying the Distributive Property.