Certainly! Let's combine the like terms in the expression:
[tex]\[ 3y + 4x^2 - 3x^2 - 2y + x^2 + 2y - 3x^3 \][/tex]
### Step-by-Step Solution:
1. Identify like terms:
- Terms with [tex]\(y\)[/tex]: [tex]\(3y, -2y,\)[/tex] and [tex]\(2y\)[/tex]
- Terms with [tex]\(x^2\)[/tex]: [tex]\(4x^2, -3x^2,\)[/tex] and [tex]\(x^2\)[/tex]
- Terms with [tex]\(x^3\)[/tex]: [tex]\(-3x^3\)[/tex] (only one term)
2. Combine the [tex]\(y\)[/tex] terms:
[tex]\[
3y - 2y + 2y
\][/tex]
We can combine these by adding or subtracting the coefficients:
[tex]\[
(3 - 2 + 2)y = 3y
\][/tex]
3. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
4x^2 - 3x^2 + x^2
\][/tex]
Similarly, combine the coefficients:
[tex]\[
(4 - 3 + 1)x^2 = 2x^2
\][/tex]
4. Combine the [tex]\(x^3\)[/tex] term:
[tex]\[
-3x^3
\][/tex]
This remains as it is because there are no other [tex]\(x^3\)[/tex] terms to combine.
5. Write the simplified expression:
Combining all the simplified like terms, we get:
[tex]\[
-3x^3 + 2x^2 + 3y
\][/tex]
Thus, the final simplified expression is:
[tex]\[
-3x^3 + 2x^2 + 3y
\][/tex]
### Solution:
[tex]\[
-3x^3 + 2x^2 + 3y
\][/tex]
