Question
Subtract. \( \left(4 y^{2}-9 y+8\right)-\left(8 y^{2}-9 y+7\right) \) \( \left(4 y^{2}-9 y+8\right)-\left(8 y^{2}-9 y+7\right)=\square \) (Simplify your answer. Do not factor.)
Ask by Olson Chadwick. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(-4y^{2} + 1\)
Solution
To subtract the two polynomials, follow these steps:
\[
\left(4 y^{2} - 9 y + 8\right) - \left(8 y^{2} - 9 y + 7\right)
\]
1. Distribute the negative sign to the second polynomial:
\[
4 y^{2} - 9 y + 8 - 8 y^{2} + 9 y - 7
\]
2. Combine like terms:
- \(4 y^{2} - 8 y^{2} = -4 y^{2}\)
- \(-9 y + 9 y = 0 y\) (these terms cancel out)
- \(8 - 7 = 1\)
3. Putting it all together:
\[
-4 y^{2} + 1
\]
**Final Answer:**
\(-4y^{2} + 1\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To subtract the expressions, start by distributing the negative sign across the second set of parentheses: \[ (4y^2 - 9y + 8) - (8y^2 - 9y + 7) = 4y^2 - 9y + 8 - 8y^2 + 9y - 7 \] Now, combine like terms: 1. For the \(y^2\) terms: \(4y^2 - 8y^2 = -4y^2\) 2. For the \(y\) terms: \(-9y + 9y = 0y\) (they cancel out) 3. For the constant terms: \(8 - 7 = 1\) Putting it all together, we have: \[ -4y^2 + 0y + 1 = -4y^2 + 1 \] So the final simplified expression is: \[ \left(4 y^{2}-9 y+8\right)-\left(8 y^{2}-9 y+7\right) = -4y^2 + 1 \]
