Question: User: 2u^2 + uv - v^2 - 4u^2 + 4uv - u^2
1. **State the problem:** Simplify the expression $$2u^2 + uv - v^2 - 4u^2 + 4uv - u^2$$.
2. **Combine like terms:** Group the terms with $$u^2$$, $$uv$$, and $$v^2$$ separately.
3. For $$u^2$$ terms: $$2u^2 - 4u^2 - u^2$$.
4. For $$uv$$ terms: $$uv + 4uv$$.
5. For $$v^2$$ term: $$-v^2$$.
6. Simplify each group:
- $$2u^2 - 4u^2 - u^2 = \cancel{2u^2} - \cancel{4u^2} - u^2 = -3u^2$$.
- $$uv + 4uv = 5uv$$.
- $$-v^2$$ remains as is.
7. **Write the simplified expression:** $$-3u^2 + 5uv - v^2$$.
8. This is the simplified form of the original expression.