Warren Matthews
05/18/2024 · Middle School
8 Add \( \left(7 x^{2}-5 x+13\right)+\left(5 x^{2}+9 x-54\right) \)
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Tutor-Verified Answer
Step-by-step Solution
To add the two polynomials \( (7x^2 - 5x + 13) \) and \( (5x^2 + 9x - 54) \), we combine like terms.
1. **Combine the \(x^2\) terms:**
\[
7x^2 + 5x^2 = 12x^2
\]
2. **Combine the \(x\) terms:**
\[
-5x + 9x = 4x
\]
3. **Combine the constant terms:**
\[
13 - 54 = -41
\]
Now, putting it all together, we have:
\[
(7x^2 - 5x + 13) + (5x^2 + 9x - 54) = 12x^2 + 4x - 41
\]
Thus, the result is:
\[
\boxed{12x^2 + 4x - 41}
\]
Quick Answer
The result is \( 12x^2 + 4x - 41 \).
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