Question
Question #10: Which expression is equivalent to `81x^{2}\ -\ 18x`?
**Hint: check each answer using the distributive property and see which one matches the expression.**
**Hint: check each answer using the distributive property and see which one matches the expression.**
Answers
GPT-4o mini
To find an expression that is equivalent to \( 81x^2 - 18x \), we can factor it.
Start by identifying the common factors in the expression:
1. The coefficients \( 81 \) and \( -18 \) have a greatest common factor (GCF) of \( 9 \).
2. Both terms contain \( x \).
We can factor out \( 9x \) from the expression:
\[
81x^2 - 18x = 9x(9x - 2)
\]
Now, let's check the factored expression \( 9x(9x - 2) \) using the distributive property to see if it matches the original expression:
\[
9x(9x - 2) = 9x \cdot 9x - 9x \cdot 2 = 81x^2 - 18x
\]
This confirms that \( 9x(9x - 2) \) is indeed equivalent to \( 81x^2 - 18x \).
Now you can verify if any answer choices match \( 9x(9x - 2) \). If you provide the answer choices, I can help you identify any corresponding options.
Start by identifying the common factors in the expression:
1. The coefficients \( 81 \) and \( -18 \) have a greatest common factor (GCF) of \( 9 \).
2. Both terms contain \( x \).
We can factor out \( 9x \) from the expression:
\[
81x^2 - 18x = 9x(9x - 2)
\]
Now, let's check the factored expression \( 9x(9x - 2) \) using the distributive property to see if it matches the original expression:
\[
9x(9x - 2) = 9x \cdot 9x - 9x \cdot 2 = 81x^2 - 18x
\]
This confirms that \( 9x(9x - 2) \) is indeed equivalent to \( 81x^2 - 18x \).
Now you can verify if any answer choices match \( 9x(9x - 2) \). If you provide the answer choices, I can help you identify any corresponding options.