Use the Distributive Property to verify which expression is equivalent to (x−5)(x−3).(1 point)
Responses
2x−2
2 x minus 2
3x2−4x2−3x−15
3 x squared minus 4 x squared minus 3 x minus 15
x2−2x+15
x squared minus 2 x plus 15
x2−8x+15
x squared minus 8 x plus 15
To verify which expression is equivalent to (x−5)(x−3), we need to distribute the factors using the Distributive Property:
(x−5)(x−3)
= x(x) + x(-3) + (-5)(x) + (-5)(-3)
= x^2 - 3x - 5x + 15
= x^2 - 8x + 15
Therefore, the expression equivalent to (x−5)(x−3) is x^2 - 8x + 15.
To verify which expression is equivalent to (x-5)(x-3) using the Distributive Property, we need to multiply each term inside the first parentheses by each term inside the second parentheses and then simplify the expression.
Let's go through each option:
1. (x-5)(x-3) = x(x) + x(-3) - 5(x) - 5(-3) = x^2 - 3x - 5x + 15 = x^2 - 8x + 15
2. 2x-2 is not a correct expression, as it does not involve multiplying each term inside the parentheses.
3. 3x^2 - 4x^2 - 3x - 15 also does not involve multiplying each term inside the parentheses.
4. x^2 - 2x + 15 does not involve multiplying each term inside the parentheses.
Therefore, the correct expression equivalent to (x-5)(x-3) using the Distributive Property is x^2 - 8x + 15.