Let's carefully review the subtraction step in the polynomial division process to understand why the answer to the subtraction $(x^2 - 1) - (x^2 - x)$ is $x - 1$.

Step-by-Step Explanation of the Subtraction

1. Write down the expressions to subtract:

   We have: $(x^2 - 1) - (x^2 - x)$

2. Distribute the negative sign across the second expression:

   Subtracting polynomials involves distributing the negative sign to each term in the polynomial being subtracted. This changes the sign of each term in the second polynomial:

   $x^2 - 1 - x^2 + x$

3. Combine like terms:

   Now, combine the like terms:

   • The $x^2$ terms: $x^2 - x^2 = 0$
   • The constant term: $-1$
   • The $x$ term: $+x$

   Combining these, we have: $0 + x - 1 = x - 1$

Result

Therefore, the result of the subtraction $(x^2 - 1) - (x^2 - x)$ is indeed $x - 1$.

This matches the step you provided, confirming that the subtraction was done correctly.

Would you like more details on this process or have any other questions?

Related Questions:

1. How do you subtract polynomials with more than two terms?
2. Why is it important to align like terms when performing polynomial subtraction?
3. What happens if you forget to distribute the negative sign when subtracting polynomials?
4. How can you use polynomial subtraction in solving polynomial equations?
5. Are there any shortcuts or techniques to make polynomial subtraction easier?

Tip: Always double-check each step in polynomial subtraction to ensure the correct distribution of negative signs and proper combination of like terms.