Sure! Let's combine the like terms in the given expression step by step.
The given expression is:
[tex]\[
-4 x^2 - 3 + 4 + 3 - 5 y^2 + 3 y^2 - 5 y^2
\][/tex]
First, we need to group the like terms together. Let's start with the [tex]\(x^2\)[/tex] terms, the constant terms, and the [tex]\(y^2\)[/tex] terms separately:
1. [tex]\(x^2\)[/tex] terms:
[tex]\[
-4 x^2
\][/tex]
We only have the term [tex]\(-4 x^2\)[/tex].
2. Constant terms:
[tex]\[
-3 + 4 + 3
\][/tex]
Adding these together:
[tex]\[
-3 + 4 = 1
\][/tex]
[tex]\[
1 + 3 = 4
\][/tex]
So, the combined constant term is [tex]\(4\)[/tex].
3. [tex]\(y^2\)[/tex] terms:
[tex]\[
-5 y^2 + 3 y^2 - 5 y^2
\][/tex]
Adding these together:
[tex]\[
-5 y^2 + 3 y^2 = -2 y^2
\][/tex]
[tex]\[
-2 y^2 - 5 y^2 = -7 y^2
\][/tex]
So, the combined [tex]\(y^2\)[/tex] term is [tex]\(-7 y^2\)[/tex].
Now, let's write the expression with the combined like terms:
[tex]\[
-4 x^2 + 4 - 7 y^2
\][/tex]
Hence, the final simplified expression is:
[tex]\[
-4 x^2 + 4 - 7 y^2
\][/tex]
