To simplify the given expression [tex]\(2y - 3x^2 + 6x^2 - 3y\)[/tex], let's follow these steps:
1. Group Like Terms: Identify and group the terms involving [tex]\(x^2\)[/tex] and [tex]\(y\)[/tex].
- The terms involving [tex]\(x^2\)[/tex] are [tex]\(-3x^2\)[/tex] and [tex]\(6x^2\)[/tex].
- The terms involving [tex]\(y\)[/tex] are [tex]\(2y\)[/tex] and [tex]\(-3y\)[/tex].
2. Combine the Constants:
- For the [tex]\(x^2\)[/tex] terms:
[tex]\[
-3x^2 + 6x^2
\][/tex]
By combining like terms, we get:
[tex]\[
-3x^2 + 6x^2 = 3x^2
\][/tex]
- For the [tex]\(y\)[/tex] terms:
[tex]\[
2y - 3y
\][/tex]
By combining like terms, we get:
[tex]\[
2y - 3y = -y
\][/tex]
3. Substitute Back: Place the simplified terms back together:
[tex]\[
3x^2 - y
\][/tex]
Based on these steps, the simplified expression for [tex]\(2y - 3x^2 + 6x^2 - 3y\)[/tex] is:
[tex]\[
3x^2 - y
\][/tex]
So, the correct option is:
[tex]\[
\boxed{3x^2 - y}
\][/tex]
