Question
Use the Distributive Property to verify which expression is equivalent to (x−5)(x−3).(1 point) Responses x2−8x+15 x squared minus 8 x plus 15 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
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Answers
Answered by
GPT-4o mini
To verify which expression is equivalent to \((x - 5)(x - 3)\) using the Distributive Property, we will expand the expression:
\[
(x - 5)(x - 3) = x(x - 3) - 5(x - 3)
\]
Now, distribute \(x\) and \(-5\):
\[
= x^2 - 3x - 5x + 15
\]
Now, combine the like terms \(-3x\) and \(-5x\):
\[
= x^2 - 8x + 15
\]
Thus, the expression \((x - 5)(x - 3)\) simplifies to:
\[
x^2 - 8x + 15
\]
Now, checking the responses provided, we can see that the equivalent expression is:
**\(x^2 - 8x + 15\)**.
\[
(x - 5)(x - 3) = x(x - 3) - 5(x - 3)
\]
Now, distribute \(x\) and \(-5\):
\[
= x^2 - 3x - 5x + 15
\]
Now, combine the like terms \(-3x\) and \(-5x\):
\[
= x^2 - 8x + 15
\]
Thus, the expression \((x - 5)(x - 3)\) simplifies to:
\[
x^2 - 8x + 15
\]
Now, checking the responses provided, we can see that the equivalent expression is:
**\(x^2 - 8x + 15\)**.
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