Question
Find the difference between the two polynomials, showing all work below.
(9x2+17x+13)−(2x2+12x+11)
(9x2+17x+13)−(2x2+12x+11)
Answers
GPT-4o mini
To find the difference between the two polynomials \( (9x^2 + 17x + 13) - (2x^2 + 12x + 11) \), we will first distribute the negative sign across the second polynomial and then combine like terms.
1. Write down the polynomials:
\[
9x^2 + 17x + 13
\]
and
\[
2x^2 + 12x + 11.
\]
2. Distribute the negative sign across the second polynomial:
\[
(9x^2 + 17x + 13) - (2x^2 + 12x + 11) = 9x^2 + 17x + 13 - 2x^2 - 12x - 11.
\]
3. Now we can rearrange and combine like terms. First, let's group the \(x^2\) terms, the \(x\) terms, and the constant terms:
\[
(9x^2 - 2x^2) + (17x - 12x) + (13 - 11).
\]
4. Now perform the operations:
- For the \(x^2\) terms:
\[
9x^2 - 2x^2 = 7x^2.
\]
- For the \(x\) terms:
\[
17x - 12x = 5x.
\]
- For the constant terms:
\[
13 - 11 = 2.
\]
5. Now we can combine everything into our final polynomial:
\[
7x^2 + 5x + 2.
\]
Therefore, the difference between the two polynomials is:
\[
\boxed{7x^2 + 5x + 2}.
\]
1. Write down the polynomials:
\[
9x^2 + 17x + 13
\]
and
\[
2x^2 + 12x + 11.
\]
2. Distribute the negative sign across the second polynomial:
\[
(9x^2 + 17x + 13) - (2x^2 + 12x + 11) = 9x^2 + 17x + 13 - 2x^2 - 12x - 11.
\]
3. Now we can rearrange and combine like terms. First, let's group the \(x^2\) terms, the \(x\) terms, and the constant terms:
\[
(9x^2 - 2x^2) + (17x - 12x) + (13 - 11).
\]
4. Now perform the operations:
- For the \(x^2\) terms:
\[
9x^2 - 2x^2 = 7x^2.
\]
- For the \(x\) terms:
\[
17x - 12x = 5x.
\]
- For the constant terms:
\[
13 - 11 = 2.
\]
5. Now we can combine everything into our final polynomial:
\[
7x^2 + 5x + 2.
\]
Therefore, the difference between the two polynomials is:
\[
\boxed{7x^2 + 5x + 2}.
\]