Sure! Let's simplify the given expression step by step by combining like terms.
The original expression is:
[tex]\[
-3x^2 - y^2 - y^2 - 5x - x^2 + 2 - 1
\][/tex]
### Step 1: Combine the [tex]\(x^2\)[/tex] terms
Here, you have [tex]\(-3x^2\)[/tex] and [tex]\(-x^2\)[/tex]. When you add them together:
[tex]\[
-3x^2 - x^2 = -4x^2
\][/tex]
### Step 2: Combine the [tex]\(y^2\)[/tex] terms
Next, you have two [tex]\(-y^2\)[/tex] terms. Adding these together:
[tex]\[
-y^2 - y^2 = -2y^2
\][/tex]
### Step 3: Combine the [tex]\(x\)[/tex] terms
You have a single [tex]\(x\)[/tex] term which is [tex]\(-5x\)[/tex], so it stays as it is:
[tex]\[
-5x
\][/tex]
### Step 4: Combine the constant terms
Finally, combine the constants [tex]\(2\)[/tex] and [tex]\(-1\)[/tex]:
[tex]\[
2 - 1 = 1
\][/tex]
### Step 5: Write the simplified expression
Putting it all together, the simplified expression is:
[tex]\[
-4x^2 - 2y^2 - 5x + 1
\][/tex]
So, the simplified form of the given expression is:
[tex]\[
-4x^2 - 2y^2 - 5x + 1
\][/tex]
