Use the Distributive Property to verify which expression is equivalent to (x−5)(x−3).(1 point)
Responses
2x−2
2 x minus 2
x2−8x+15
x squared minus 8 x plus 15
x2−2x+15
x squared minus 2 x plus 15
3x2−4x2−3x−15
The expression that is equivalent to (x−5)(x−3) using the Distributive Property is x2−8x+15.
To use the Distributive Property to verify the equivalent expression to (x-5)(x-3), we need to expand the given expression.
(x-5)(x-3) can be expanded as follows:
(x)(x) + (x)(-3) + (-5)(x) + (-5)(-3)
Simplifying this expression, we get:
x^2 - 3x - 5x + 15
Combining like terms, we have:
x^2 - 8x + 15
Therefore, the expression x^2 - 8x + 15 is equivalent to (x-5)(x-3).
To use the Distributive Property, you need to multiply each term in the first set of parentheses by each term in the second set of parentheses and then combine like terms.
Let's follow the steps to verify which expression is equivalent to (x−5)(x−3):
Step 1: Distribute the first term in the first set of parentheses (x) to both terms in the second set of parentheses (x and -3):
x * x = x^2
x * -3 = -3x
Step 2: Distribute the second term in the first set of parentheses (-5) to both terms in the second set of parentheses (x and -3):
-5 * x = -5x
-5 * -3 = 15
Now, combine like terms:
x^2 + (-3x) + (-5x) + 15
Next, simplify the expression:
x^2 - 3x - 5x + 15
Combine like terms once more:
x^2 - 8x + 15
Therefore, the expression that is equivalent to (x−5)(x−3) is x^2 - 8x + 15.