Subtract. $$ \begin{array}{r}8 y^{2}-6 y+5 \ \frac{-\left(-2 y^{2}+6 y+9 ight)}{} \ \hline \frac{-\left(-2 y^{2}+6 y+9 ight)}{\square}\end{array} $$

Question

Subtract. $$ \begin{array}{r}8 y^{2}-6 y+5 \ \frac{-\left(-2 y^{2}+6 y+9ight)}{} \ \hline \frac{-\left(-2 y^{2}+6 y+9ight)}{\square}\end{array} $$

UpStudy AI · Accepted Answer

Sure, let's perform the subtraction step by step.

**Given:**
$$
\begin{array}{r}
8 y^{2} - 6 y + 5 \
- \left(-2 y^{2} + 6 y + 9\right) \
\hline
\end{array}
$$

**Step 1: Distribute the Negative Sign**

When you subtract a polynomial, it's equivalent to adding its negative. So, distribute the negative sign to each term inside the parentheses:

$$
- \left(-2 y^{2} + 6 y + 9\right) = 2 y^{2} - 6 y - 9
$$

**Step 2: Rewrite the Expression**

Now, rewrite the original expression with the distributed terms:

$$
8 y^{2} - 6 y + 5 + 2 y^{2} - 6 y - 9
$$

**Step 3: Combine Like Terms**

Combine the coefficients of like terms:

- **$$ y^{2} $$ terms:**
  $$
  8 y^{2} + 2 y^{2} = 10 y^{2}
  $$

- **$$ y $$ terms:**
  $$
  -6 y - 6 y = -12 y
  $$

- **Constant terms:**
  $$
  5 - 9 = -4
  $$

**Step 4: Write the Final Result**

Putting it all together:

$$
10 y^{2} - 12 y - 4
$$

**Final Answer:**
$$
10 y^{2} - 12 y - 4
$$
The result of the subtraction is $$10y^{2} - 12y - 4$$.

Subtract. \( \begin{array}{r}8 y^{2}-6 y+5 \\ \frac{-\left(-2 y^{2}+6 y+9\right)}{} \\ \hline \frac{-\left(-2 y^{2}+6 y+9\right)}{\square}\end{array} \)