4:24AM Fri Jan 24 \( \begin{array}{r}\text { 16. [-/1 Points] DETAILS MY NOTES TGEIALG6 5.5.097, } \\ \text { Perform the operation. (Simplify your answer completely.) } \\ \begin{array}{r}2 x^{3} y^{2}+9 x^{2} y+6 x+17 \\ -\left(-7 x^{3} y^{2}+2 x^{2} y+4 x-2\right)\end{array} \\ \text { SUBMIT ANSWER }\end{array} \)

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:** \[ 9x^{3} y^{2} + 7x^{2} y + 2x + 19 \]