Question
Use the Distributive Property to write the expression 4x2 - 36 a different way. (1 point)
O (2x + 9) (x - 9)
O (2x + 6) (2x - 6)
• (x + 18) x - 18)
• 4x (х - 9)
O (2x + 9) (x - 9)
O (2x + 6) (2x - 6)
• (x + 18) x - 18)
• 4x (х - 9)
Answers
Answer
It’s not that one remember that distributing means to multiply both terms by 4 and x
Answered by
GPT-4o mini
To use the Distributive Property to factor the expression \(4x^2 - 36\), we can factor out a common factor and look for a difference of squares.
1. Notice that \(4x^2 - 36\) can be rewritten as \(4(x^2 - 9)\).
2. The expression \(x^2 - 9\) is a difference of squares, which can be factored into \((x + 3)(x - 3)\).
Thus, the full factorization of the expression is:
\[
4(x + 3)(x - 3)
\]
Looking at the options provided, we can see that this factorization is equivalent to:
- \(4(x - 9)\)
Therefore, the answer is:
**4x (x - 9)**.
1. Notice that \(4x^2 - 36\) can be rewritten as \(4(x^2 - 9)\).
2. The expression \(x^2 - 9\) is a difference of squares, which can be factored into \((x + 3)(x - 3)\).
Thus, the full factorization of the expression is:
\[
4(x + 3)(x - 3)
\]
Looking at the options provided, we can see that this factorization is equivalent to:
- \(4(x - 9)\)
Therefore, the answer is:
**4x (x - 9)**.
Answered by
GPT-4o mini
Apologies for the oversight regarding the distribution aspect. Let's factor \(4x^2 - 36\) properly using the Distributive Property.
The expression \(4x^2 - 36\) can be factored using the difference of squares.
1. Recognize that \(36\) can be rewritten as \(6^2\).
2. The expression can thus be seen as \(4(x^2 - 9)\) where \(x^2 - 9\) is again a difference of squares.
However, it looks like you're emphasizing the need to view this from a distribution perspective rather than only reaching to the simplest factoring. In this case:
1. First factor out the common term \(4\) from the expression:
\[
4(x^2 - 9)
\]
Now, realizing that \( (x^2 - 9) \) is actually a difference of squares, but if we consider distributing \(4\) and \(6\) (since we want to maintain the original expression structure), we can assess the other options again based on re-expansion.
Yet, looking at the options provided:
1. \( (2x + 6)(2x - 6) \) distributes back to \( 4x^2 - 36 \).
2. \( (2x + 9)(x - 9) \) does not work.
3. \( (x + 18)(x - 18) \) does not work either.
4. \( 4x(x - 9) \) doesn’t expand to \( 4x^2 - 36 \).
So the correct factorization from your choices should be:
**(2x + 6)(2x - 6)**.
This shows the proper distributive formatting back out to \(4x^2 - 36\). Thank you for your understanding!
The expression \(4x^2 - 36\) can be factored using the difference of squares.
1. Recognize that \(36\) can be rewritten as \(6^2\).
2. The expression can thus be seen as \(4(x^2 - 9)\) where \(x^2 - 9\) is again a difference of squares.
However, it looks like you're emphasizing the need to view this from a distribution perspective rather than only reaching to the simplest factoring. In this case:
1. First factor out the common term \(4\) from the expression:
\[
4(x^2 - 9)
\]
Now, realizing that \( (x^2 - 9) \) is actually a difference of squares, but if we consider distributing \(4\) and \(6\) (since we want to maintain the original expression structure), we can assess the other options again based on re-expansion.
Yet, looking at the options provided:
1. \( (2x + 6)(2x - 6) \) distributes back to \( 4x^2 - 36 \).
2. \( (2x + 9)(x - 9) \) does not work.
3. \( (x + 18)(x - 18) \) does not work either.
4. \( 4x(x - 9) \) doesn’t expand to \( 4x^2 - 36 \).
So the correct factorization from your choices should be:
**(2x + 6)(2x - 6)**.
This shows the proper distributive formatting back out to \(4x^2 - 36\). Thank you for your understanding!
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