Let’s simplify the given expressions step by step.

a) $(-x^2 + 2x - 4) + (-2x + 3)$

Combine like terms:

• Combine $x^2$: $-x^2$
• Combine $x$: $2x - 2x = 0$
• Combine constants: $-4 + 3 = -1$

Simplified form: $-x^2 - 1$

b) $(x^2 - x + 5) - (3x^2 + x - 1)$

Distribute the negative sign to the second parentheses: $(x^2 - x + 5) - 3x^2 - x + 1$

Combine like terms:

• Combine $x^2$: $x^2 - 3x^2 = -2x^2$
• Combine $x$: $-x - x = -2x$
• Combine constants: $5 + 1 = 6$

Simplified form: $-2x^2 - 2x + 6$

c) $(x^2 - 3x + 1) - (-x^2 - 1)$

Distribute the negative sign to the second parentheses: $(x^2 - 3x + 1) + x^2 + 1$

Combine like terms:

• Combine $x^2$: $x^2 + x^2 = 2x^2$
• Combine $x$: $-3x$
• Combine constants: $1 + 1 = 2$

Simplified form: $2x^2 - 3x + 2$

Final Results:

1. a) $-x^2 - 1$
2. b) $-2x^2 - 2x + 6$
3. c) $2x^2 - 3x + 2$

Would you like a detailed breakdown of any part?

Related Questions:

1. Can you factorize the results of each simplification?
2. How do these simplifications work in terms of polynomial degrees?
3. How can these results be visualized on a graph?
4. What happens if you equate any of these simplified expressions to zero?
5. Are there specific contexts where these simplified forms are particularly useful?

Tip:

Always carefully distribute negative signs when simplifying, as they can easily lead to mistakes if overlooked!