Question
Subtract and simplify the following: \[ \left(8 a^{2}-5 a+7\right)-\left(a^{2}+9 a-1\right) \] Select the correct answer below: \( 7 a^{2}-14 a+6 \) \( 7 a^{2}-14 a+8 \) \( 7 a^{2}+4 a+8 \) \( 7 a^{2}+4 a+6 \) \( 7 a^{2}+14 a+8 \)
Ask by Weber Burton. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \(7a^2 - 14a + 8\).
Solution
1. Write the expression:
\[
\left(8a^2 - 5a + 7\right) - \left(a^2 + 9a - 1\right)
\]
2. Distribute the negative sign in the second parentheses:
\[
8a^2 - 5a + 7 - a^2 - 9a + 1
\]
3. Combine like terms:
- Combine the \(a^2\) terms:
\[
8a^2 - a^2 = 7a^2
\]
- Combine the \(a\) terms:
\[
-5a - 9a = -14a
\]
- Combine the constant terms:
\[
7 + 1 = 8
\]
4. Thus, the simplified expression is:
\[
7a^2 - 14a + 8
\]
The correct answer is:
\[
7a^2 - 14a + 8
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
First, let's simplify the expression \( \left(8 a^{2}-5 a+7\right)-\left(a^{2}+9 a-1\right) \). We start by distributing the minus sign in front of the second parentheses: \[ 8 a^{2} - 5 a + 7 - a^{2} - 9 a + 1 \] Now, we can combine like terms. For the \( a^{2} \) terms: \[ 8 a^{2} - a^{2} = 7 a^{2} \] For the \( a \) terms: \[ -5 a - 9 a = -14 a \] And for the constant terms: \[ 7 + 1 = 8 \] Putting it all together, we have: \[ 7 a^{2} - 14 a + 8 \] So the correct answer is: \( 7 a^{2} - 14 a + 8 \)
