Question
Which of the following correctly simplifies (9x^2+17x+13)−(2x^2+12x+11)
?(1 point)
Responses
9x2+17x+13−2x2−12x−11
9 x squared plus 17 x plus 13 minus 2 x squared minus 12 x minus 11
12x2+2
12 x squared plus 2
7x2+5x+2
7 x squared plus 5 x plus 2
7x2+29x+24
7 x squared plus 29 x plus 24
?(1 point)
Responses
9x2+17x+13−2x2−12x−11
9 x squared plus 17 x plus 13 minus 2 x squared minus 12 x minus 11
12x2+2
12 x squared plus 2
7x2+5x+2
7 x squared plus 5 x plus 2
7x2+29x+24
7 x squared plus 29 x plus 24
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To simplify the expression \((9x^2 + 17x + 13) - (2x^2 + 12x + 11)\), we first distribute the negative sign across the second group:
\[
(9x^2 + 17x + 13) - (2x^2 + 12x + 11) = 9x^2 + 17x + 13 - 2x^2 - 12x - 11
\]
Now, we can combine like terms:
1. **Combine the \(x^2\) terms**:
\[
9x^2 - 2x^2 = 7x^2
\]
2. **Combine the \(x\) terms**:
\[
17x - 12x = 5x
\]
3. **Combine the constant terms**:
\[
13 - 11 = 2
\]
Putting it all together, we have:
\[
7x^2 + 5x + 2
\]
Thus, the correctly simplified expression is:
**7x² + 5x + 2** (which matches the option "7x2+5x+2").
\[
(9x^2 + 17x + 13) - (2x^2 + 12x + 11) = 9x^2 + 17x + 13 - 2x^2 - 12x - 11
\]
Now, we can combine like terms:
1. **Combine the \(x^2\) terms**:
\[
9x^2 - 2x^2 = 7x^2
\]
2. **Combine the \(x\) terms**:
\[
17x - 12x = 5x
\]
3. **Combine the constant terms**:
\[
13 - 11 = 2
\]
Putting it all together, we have:
\[
7x^2 + 5x + 2
\]
Thus, the correctly simplified expression is:
**7x² + 5x + 2** (which matches the option "7x2+5x+2").
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