Question
What correctly simplifies (9x^2 + 17x + 13) – (2x^2 + 12x + 11)?
Answers
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Answered by
GPT-4o mini
To simplify the expression \((9x^2 + 17x + 13) - (2x^2 + 12x + 11)\), we'll start by distributing the negative sign across the second polynomial:
\[
(9x^2 + 17x + 13) - (2x^2 + 12x + 11) = 9x^2 + 17x + 13 - 2x^2 - 12x - 11
\]
Next, we can group the 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:
\[
13 - 11 = 2
\]
Now, we can write the simplified expression by adding these results together:
\[
7x^2 + 5x + 2
\]
Thus, the final simplified expression is
\[
\boxed{7x^2 + 5x + 2}
\]
\[
(9x^2 + 17x + 13) - (2x^2 + 12x + 11) = 9x^2 + 17x + 13 - 2x^2 - 12x - 11
\]
Next, we can group the 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:
\[
13 - 11 = 2
\]
Now, we can write the simplified expression by adding these results together:
\[
7x^2 + 5x + 2
\]
Thus, the final simplified expression is
\[
\boxed{7x^2 + 5x + 2}
\]
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