To simplify the expression [tex]\(\left(3 w^2 - 2 z^2 + 3 w\right) - \left(w^2 + 2 z^2 + 3 w\right)\)[/tex], follow these steps:
1. Distribute the subtraction:
[tex]\[
\left(3 w^2 - 2 z^2 + 3 w\right) - \left(w^2 + 2 z^2 + 3 w\right) = 3 w^2 - 2 z^2 + 3 w - w^2 - 2 z^2 - 3 w.
\][/tex]
2. Combine like terms:
- Combine the [tex]\(w^2\)[/tex] terms:
[tex]\[
3 w^2 - w^2 = (3 - 1) w^2 = 2 w^2.
\][/tex]
- Combine the [tex]\(z^2\)[/tex] terms:
[tex]\[
-2 z^2 - 2 z^2 = (-2 - 2) z^2 = -4 z^2.
\][/tex]
- Combine the [tex]\(w\)[/tex] terms:
[tex]\[
3 w - 3 w = 0.
\][/tex]
3. Write the simplified expression:
[tex]\[
2 w^2 - 4 z^2.
\][/tex]
Hence, the simplified expression is [tex]\(\boxed{2 w^2 - 4 z^2}\)[/tex].
