Question
4:24AM Fri Jan 24 \( \begin{array}{r}\text { 16. [-/1 Points] DETAILS MY NOTES TGEIALG6 5.5.097, } \\ \text { Perform the operation. (Simplify your answer completely.) } \\ \begin{array}{r}2 x^{3} y^{2}+9 x^{2} y+6 x+17 \\ -\left(-7 x^{3} y^{2}+2 x^{2} y+4 x-2\right)\end{array} \\ \text { SUBMIT ANSWER }\end{array} \)
Ask by Cox Thornton. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified expression is \(9x^{3} y^{2} + 7x^{2} y + 2x + 19\).
Solution
To simplify the given expression, follow these steps:
**Original Expression:**
\[
\begin{align*}
2x^{3} y^{2} + 9x^{2} y + 6x + 17 \\
- \left( -7x^{3} y^{2} + 2x^{2} y + 4x - 2 \right)
\end{align*}
\]
**Step 1: Distribute the Negative Sign**
\[
2x^{3} y^{2} + 9x^{2} y + 6x + 17 + 7x^{3} y^{2} - 2x^{2} y - 4x + 2
\]
**Step 2: Combine Like Terms**
- **\(x^{3} y^{2}\) terms:**
\[
2x^{3} y^{2} + 7x^{3} y^{2} = 9x^{3} y^{2}
\]
- **\(x^{2} y\) terms:**
\[
9x^{2} y - 2x^{2} y = 7x^{2} y
\]
- **\(x\) terms:**
\[
6x - 4x = 2x
\]
- **Constant terms:**
\[
17 + 2 = 19
\]
**Step 3: Write the Simplified Expression**
\[
9x^{3} y^{2} + 7x^{2} y + 2x + 19
\]
**Final Answer:**
\[
9x^{3} y^{2} + 7x^{2} y + 2x + 19
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To perform the operation and simplify the expression, first rewrite the given expression clearly. You have: \( 2x^{3}y^{2} + 9x^{2}y + 6x + 17 - \left(-7x^{3}y^{2} + 2x^{2}y + 4x - 2\right) \) Now, distribute the negative sign in front of the parentheses: \( 2x^{3}y^{2} + 9x^{2}y + 6x + 17 + 7x^{3}y^{2} - 2x^{2}y - 4x + 2 \) Combine like terms: 1. For \(x^{3}y^{2}\): \(2x^{3}y^{2} + 7x^{3}y^{2} = 9x^{3}y^{2}\) 2. For \(x^{2}y\): \(9x^{2}y - 2x^{2}y = 7x^{2}y\) 3. For \(x\): \(6x - 4x = 2x\) 4. For the constant term: \(17 + 2 = 19\) Putting it all together gives you: \(9x^{3}y^{2} + 7x^{2}y + 2x + 19\) So, the simplified answer is: \(9x^{3}y^{2} + 7x^{2}y + 2x + 19\)
