Asked by goku
Multiply the polynomials (2r−5)(r+4) .(2 points)
_r2+_ r + _
_r2+_ r + _
Answers
Answered by
GPT-4o mini
To multiply the polynomials \( (2r - 5)(r + 4) \), we can use the distributive property (also known as the FOIL method for binomials).
1. Multiply the first terms:
\[ 2r \cdot r = 2r^2 \]
2. Multiply the outer terms:
\[ 2r \cdot 4 = 8r \]
3. Multiply the inner terms:
\[ -5 \cdot r = -5r \]
4. Multiply the last terms:
\[ -5 \cdot 4 = -20 \]
Now, we combine all these results together:
\[ 2r^2 + 8r - 5r - 20 \]
Combine the like terms \( 8r - 5r \):
\[ 2r^2 + 3r - 20 \]
So, the result of multiplying the polynomials is:
\[
\boxed{2r^2 + 3r - 20}
\]
1. Multiply the first terms:
\[ 2r \cdot r = 2r^2 \]
2. Multiply the outer terms:
\[ 2r \cdot 4 = 8r \]
3. Multiply the inner terms:
\[ -5 \cdot r = -5r \]
4. Multiply the last terms:
\[ -5 \cdot 4 = -20 \]
Now, we combine all these results together:
\[ 2r^2 + 8r - 5r - 20 \]
Combine the like terms \( 8r - 5r \):
\[ 2r^2 + 3r - 20 \]
So, the result of multiplying the polynomials is:
\[
\boxed{2r^2 + 3r - 20}
\]
Answered by
GPT-4o mini
I understand that you're looking for a representation without the negative sign in the answer form. Let’s confirm it logically while adjusting the formatting according to your instructions.
After correctly multiplying the polynomials \( (2r - 5)(r + 4) \), we got:
1. \( 2r \cdot r = 2r^2 \)
2. \( 2r \cdot 4 = 8r \)
3. \( -5 \cdot r = -5r \)
4. \( -5 \cdot 4 = -20 \)
We then combined the results:
\[ 2r^2 + 8r - 5r - 20 \]
This leads to:
\[ 2r^2 + (8r - 5r) - 20 = 2r^2 + 3r - 20 \]
Now you emphasized that the answer should not have a minus in it. We will focus instead just on the structural components, leaving out the context of subtraction:
So arranging it without explicitly showing "minus," we could represent it as:
\( 2r^2 + 3r + (-20) \)
However, keep in mind that \( -20 \) is a necessary part of the polynomial, and every term must reflect the actual output of this multiplication.
In the standard polynomial form, it is:
\[
\boxed{2r^2 + 3r - 20}
\]
If you need a specific way to present this, please clarify, and I'd be glad to assist!
After correctly multiplying the polynomials \( (2r - 5)(r + 4) \), we got:
1. \( 2r \cdot r = 2r^2 \)
2. \( 2r \cdot 4 = 8r \)
3. \( -5 \cdot r = -5r \)
4. \( -5 \cdot 4 = -20 \)
We then combined the results:
\[ 2r^2 + 8r - 5r - 20 \]
This leads to:
\[ 2r^2 + (8r - 5r) - 20 = 2r^2 + 3r - 20 \]
Now you emphasized that the answer should not have a minus in it. We will focus instead just on the structural components, leaving out the context of subtraction:
So arranging it without explicitly showing "minus," we could represent it as:
\( 2r^2 + 3r + (-20) \)
However, keep in mind that \( -20 \) is a necessary part of the polynomial, and every term must reflect the actual output of this multiplication.
In the standard polynomial form, it is:
\[
\boxed{2r^2 + 3r - 20}
\]
If you need a specific way to present this, please clarify, and I'd be glad to assist!
Answered by
GPT-4o mini
I apologize for any confusion! Let's clarify the process and outcome of the multiplication step by step to ensure we're on the same page.
Given the polynomials \( (2r - 5)(r + 4) \):
1. Using the distributive property (or FOIL method):
- **First**: \( 2r \cdot r = 2r^2 \)
- **Outer**: \( 2r \cdot 4 = 8r \)
- **Inner**: \( -5 \cdot r = -5r \)
- **Last**: \( -5 \cdot 4 = -20 \)
Now, assembling these gives us:
\[
2r^2 + 8r - 5r - 20
\]
Combining like terms:
\[
2r^2 + (8r - 5r) - 20
\]
\[
2r^2 + 3r - 20
\]
If you're looking for an expression without the negative sign for the constant term, we can express it differently, though the mathematical result does indeed contain \( -20 \). However, if you need it presented without a negative sign in writing, based on the context, we can only change the presentation, not the mathematical outcome.
So to answer directly, while respecting all mathematical values, the polynomial is:
\[
\boxed{2r^2 + 3r - 20}
\]
If you require a different representation or context, such as adding a positive term in a different format, please guide me, and I’ll assist accordingly!
Given the polynomials \( (2r - 5)(r + 4) \):
1. Using the distributive property (or FOIL method):
- **First**: \( 2r \cdot r = 2r^2 \)
- **Outer**: \( 2r \cdot 4 = 8r \)
- **Inner**: \( -5 \cdot r = -5r \)
- **Last**: \( -5 \cdot 4 = -20 \)
Now, assembling these gives us:
\[
2r^2 + 8r - 5r - 20
\]
Combining like terms:
\[
2r^2 + (8r - 5r) - 20
\]
\[
2r^2 + 3r - 20
\]
If you're looking for an expression without the negative sign for the constant term, we can express it differently, though the mathematical result does indeed contain \( -20 \). However, if you need it presented without a negative sign in writing, based on the context, we can only change the presentation, not the mathematical outcome.
So to answer directly, while respecting all mathematical values, the polynomial is:
\[
\boxed{2r^2 + 3r - 20}
\]
If you require a different representation or context, such as adding a positive term in a different format, please guide me, and I’ll assist accordingly!