se the Distributive Property to verify which expression is equivalent to (x−5)(x−3).
The Distributive Property states that for any three numbers a, b, and c, a(b+c) = ab + ac.
Using this property, we can expand (x−5)(x−3):
(x−5)(x−3) = x(x−3) - 5(x−3)
Now, let's distribute the x and -5:
= x*x - 3*x - 5*x + 5*3
= x^2 - 3x - 5x + 15
Combining like terms, we get:
= x^2 - 8x + 15
Therefore, the expression that is equivalent to (x−5)(x−3) is x^2 - 8x + 15.
To use the Distributive Property, we will do the following steps:
Step 1: Distribute the first term (x) to both terms inside the second parentheses (x−3):
x(x−3)
Step 2: Distribute the second term (-5) to both terms inside the second parentheses (x−3):
-5(x−3)
Now, let's simplify each expression:
Expression 1: x(x−3)
Expanding this expression, we get:
x^2 − 3x
Expression 2: -5(x−3)
Expanding this expression, we get:
-5x + 15
So, to verify which expression is equivalent to (x−5)(x−3), we compare it with these two simplified expressions:
(x−5)(x−3) = x^2 − 3x - 5x + 15
= x^2 - 8x + 15
Therefore, the expression equivalent to (x−5)(x−3) is x^2 - 8x + 15.