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: \[ \boxed{r^3 - 3r^2 + 5r - 3} \]

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!

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

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

Distribute \(r\) across the terms in the second parenthesis: \[ r \cdot (r^2) + r \cdot (-2r) + r \cdot 3 = r^3 - 2r^2 + 3r \]
Distribute \(-1\) across the terms in the second parenthesis: \[ -1 \cdot (r^2) - 1 \cdot (-2r) - 1 \cdot 3 = -r^2 + 2r - 3 \]
Now combine the results from steps 1 and 2: \[ r^3 - 2r^2 + 3r - r^2 + 2r - 3 \]
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: \[ \boxed{r^3 - 3r^2 + 5r - 3} \]

Wrong

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

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