Question
Use the Distributive Property to rewrite the expression (2x−2)(x−6) .(1 point)
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GPT-4o mini
To rewrite the expression \((2x - 2)(x - 6)\) using the Distributive Property, we will distribute each term in the first parenthesis to each term in the second parenthesis.
Start with:
\[
(2x - 2)(x - 6)
\]
Distributing \(2x\) to both \(x\) and \(-6\):
\[
2x \cdot x + 2x \cdot (-6) = 2x^2 - 12x
\]
Now, distribute \(-2\) to both \(x\) and \(-6\):
\[
-2 \cdot x + (-2) \cdot (-6) = -2x + 12
\]
Now, combine all the terms:
\[
2x^2 - 12x - 2x + 12
\]
Combine the like terms \(-12x\) and \(-2x\):
\[
2x^2 - 14x + 12
\]
So, the expression \((2x - 2)(x - 6)\) rewritten using the Distributive Property is:
\[
2x^2 - 14x + 12
\]
Start with:
\[
(2x - 2)(x - 6)
\]
Distributing \(2x\) to both \(x\) and \(-6\):
\[
2x \cdot x + 2x \cdot (-6) = 2x^2 - 12x
\]
Now, distribute \(-2\) to both \(x\) and \(-6\):
\[
-2 \cdot x + (-2) \cdot (-6) = -2x + 12
\]
Now, combine all the terms:
\[
2x^2 - 12x - 2x + 12
\]
Combine the like terms \(-12x\) and \(-2x\):
\[
2x^2 - 14x + 12
\]
So, the expression \((2x - 2)(x - 6)\) rewritten using the Distributive Property is:
\[
2x^2 - 14x + 12
\]
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