Perform the operation. $$ \left(-8 x^{2}+3\right)+\left(x^{2}+3 x-8\right) $$

Question

UpStudy AI · Accepted Answer

To perform the addition of the two polynomials:

$$
\left(-8 x^{2} + 3\right) + \left(x^{2} + 3 x - 8\right)
$$

**Step 1: Remove the Parentheses**

Since both sets of parentheses are preceded by a plus sign, you can remove them directly:

$$
-8x^{2} + 3 + x^{2} + 3x - 8
$$

**Step 2: Combine Like Terms**

1. **Combine the $$x^2$$ terms:**
   $$
   -8x^{2} + x^{2} = -7x^{2}
   $$

2. **Combine the $$x$$ terms:**
   $$
   3x \quad (\text{only one $$x$$ term})
   $$

3. **Combine the constant terms:**
   $$
   3 - 8 = -5
   $$

**Step 3: Write the Simplified Expression**

Putting it all together:

$$
-7x^{2} + 3x - 5
$$

**Final Answer:**

$$
-7x^{2} + 3x - 5
$$
$$ -7x^{2} + 3x - 5 $$

Perform the operation. \[ \left(-8 x^{2}+3\right)+\left(x^{2}+3 x-8\right) \]