To solve the given expression, we need to first simplify it step-by-step. Let's break it down to its components and simplify accordingly.
The given expression is:
[tex]\[
\left(3a^2 - 5ab + b^2\right) - \left(-3a^2 + 2b^2 + 8ab\right)
\][/tex]
Here are the steps to simplify it:
### Step 1: Distribute the negative sign into the second group
First, we distribute the negative sign into the second parenthesis:
[tex]\[
= 3a^2 - 5ab + b^2 - (-3a^2 + 2b^2 + 8ab)
\][/tex]
This results in:
[tex]\[
= 3a^2 - 5ab + b^2 + 3a^2 - 2b^2 - 8ab
\][/tex]
### Step 2: Combine like terms
Next, we combine like terms:
- Combine the [tex]\(a^2\)[/tex] terms:
[tex]\[
= 3a^2 + 3a^2 = 6a^2
\][/tex]
- Combine the [tex]\(ab\)[/tex] terms:
[tex]\[
= -5ab - 8ab = -13ab
\][/tex]
- Combine the [tex]\(b^2\)[/tex] terms:
[tex]\[
= b^2 - 2b^2 = -b^2
\][/tex]
### Step 3: Write the simplified expression
Now, we put all the combined terms together:
[tex]\[
6a^2 - 13ab - b^2
\][/tex]
So, the simplified expression is:
[tex]\[
6a^2 - 13ab - b^2
\][/tex]
