Let's simplify the given expression step by step:
Given expression:
[tex]\[
4 - 5x^2 - 3y^3 + 7y^3 - 5 + 1 - y^3
\][/tex]
1. Combine like terms:
First, let's identify and combine the constants and the terms involving [tex]\( y^3 \)[/tex].
- The constants are: [tex]\( 4 - 5 + 1 \)[/tex].
- The terms involving [tex]\( y^3 \)[/tex] are: [tex]\( -3y^3 + 7y^3 - y^3 \)[/tex].
2. Simplify the constants:
[tex]\[
4 - 5 + 1 = 0
\][/tex]
3. Simplify the terms involving [tex]\( y^3 \)[/tex]:
[tex]\[
-3y^3 + 7y^3 - y^3 = (7 - 3 - 1)y^3 = 3y^3
\][/tex]
4. Combine the [tex]\(x^2\)[/tex] term with itself, if any:
The term involving [tex]\( x^2 \)[/tex] is simply [tex]\(-5x^2\)[/tex], and it remains unchanged.
After combining all like terms, the simplified expression is:
[tex]\[
-5x^2 + 3y^3
\][/tex]
Therefore, the result is:
[tex]\[
-5x^2 + 3y^3
\][/tex]
