To simplify the expression \(2x + 3y^2 - 2(x - y^2)\), we will proceed step-by-step:
1. Begin with the original expression:
[tex]\[
2x + 3y^2 - 2(x - y^2)
\][/tex]
2. Distribute the \(-2\) across the terms inside the parenthesis:
[tex]\[
-2(x - y^2) = -2x + 2y^2
\][/tex]
3. Substitute this back into the original expression:
[tex]\[
2x + 3y^2 - 2x + 2y^2
\][/tex]
4. Combine like terms. First, combine the \(x\) terms:
[tex]\[
2x - 2x = 0
\][/tex]
So the expression simplifies to:
[tex]\[
3y^2 + 2y^2
\][/tex]
5. Next, combine the \(y^2\) terms:
[tex]\[
3y^2 + 2y^2 = 5y^2
\][/tex]
Therefore, the simplified form of the given expression is:
[tex]\[
5y^2
\][/tex]
