Question

(r-1)(r^2-2r+3)

Answer 1

Wrong

Answer 2

To simplify the expression \((r-1)(r^2-2r+3)\), we can use the distributive property (also known as the FOIL method for binomials).

1. Distribute \(r\) across the terms in the second parenthesis:
\[
r \cdot (r^2) + r \cdot (-2r) + r \cdot 3 = r^3 - 2r^2 + 3r
\]

2. Distribute \(-1\) across the terms in the second parenthesis:
\[
-1 \cdot (r^2) - 1 \cdot (-2r) - 1 \cdot 3 = -r^2 + 2r - 3
\]

3. Now combine the results from steps 1 and 2:
\[
r^3 - 2r^2 + 3r - r^2 + 2r - 3
\]

4. Combine like terms:
- The \(r^2\) terms: \(-2r^2 - r^2 = -3r^2\)
- The \(r\) terms: \(3r + 2r = 5r\)

Putting it all together, we have:
\[
r^3 - 3r^2 + 5r - 3
\]

Thus, the simplified form of the expression \((r-1)(r^2-2r+3)\) is:
\[
\boxed{r^3 - 3r^2 + 5r - 3}
\]

Answer 3

Let’s work through the expression \((r-1)(r^2 - 2r + 3)\) step-by-step again to ensure accuracy:

1. Distributing \(r\) over each term in the polynomial \(r^2 - 2r + 3\):
\[
r \cdot r^2 + r \cdot (-2r) + r \cdot 3 = r^3 - 2r^2 + 3r
\]

2. Distributing \(-1\) over each term in the polynomial \(r^2 - 2r + 3\):
\[
-1 \cdot r^2 + (-1) \cdot (-2r) + (-1) \cdot 3 = -r^2 + 2r - 3
\]

3. Now, we combine all the results:
\[
r^3 - 2r^2 + 3r - r^2 + 2r - 3
\]

Now we combine like terms:

- Combine the \(r^2\) terms:
\[-2r^2 - r^2 = -3r^2\]

- Combine the \(r\) terms:
\[3r + 2r = 5r\]

So the complete expression now looks like:
\[
r^3 - 3r^2 + 5r - 3
\]

This means my previous response was indeed correct. Therefore, the simplified expression is:
\[
\boxed{r^3 - 3r^2 + 5r - 3}
\]

If there's a specific point of confusion or further detail you would like, please let me know!