Question
5.5 HW Adding and... men hoop earrings c... Dashboard I OUMoo... Sc 17. [0/1 Points] DETAILS MY NOTES TGEIALG6 5.5.100. Perform the operations. (Simplify your answer completely.) \[ \left(-3 z^{2}-3 z+6\right)+\left(5 z^{2}+6 z-7\right)-\left(5 z^{2}-5 z+6\right) \] \( \square \) SUBMIT ANSWER
Ask by Mathis Horton. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
-3z^{2} + 8z - 7
\]
Solution
To simplify the expression:
\[
\left(-3 z^{2} - 3 z + 6\right) + \left(5 z^{2} + 6 z - 7\right) - \left(5 z^{2} - 5 z + 6\right)
\]
**Step-by-Step Simplification:**
1. **Combine the first two polynomials:**
\[
(-3z^{2} + 5z^{2}) + (-3z + 6z) + (6 - 7) = 2z^{2} + 3z - 1
\]
2. **Subtract the third polynomial:**
\[
(2z^{2} + 3z - 1) - (5z^{2} - 5z + 6) = 2z^{2} - 5z^{2} + 3z + 5z - 1 - 6 = -3z^{2} + 8z - 7
\]
**Final Answer:**
\[
-3z^{2} + 8z - 7
\]
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Simplify this solution Mind Expander
To simplify the expression \(\left(-3 z^{2}-3 z+6\right)+\left(5 z^{2}+6 z-7\right)-\left(5 z^{2}-5 z+6\right)\), start by distributing the negative sign across the last parentheses. This gives you: \[ -3z^2 - 3z + 6 + 5z^2 + 6z - 7 - 5z^2 + 5z - 6 \] Next, combine like terms: 1. For \(z^2\): \(-3z^2 + 5z^2 - 5z^2 = -3z^2\) 2. For \(z\): \(-3z + 6z + 5z = 8z\) 3. For the constants: \(6 - 7 - 6 = -7\) Putting it all together, the simplified expression is: \[ -3z^2 + 8z - 7 \]
