Question

Multiply the polynomial expression
(r-1)(r^2-2r+3)

Answer 1

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

1. Distribute \(r\) to each term in \(r^2 - 2r + 3\):
\[
r \cdot r^2 = r^3
\]
\[
r \cdot (-2r) = -2r^2
\]
\[
r \cdot 3 = 3r
\]

So, the result of this part is:
\[
r^3 - 2r^2 + 3r
\]

2. Now, distribute \(-1\) to each term in \(r^2 - 2r + 3\):
\[
-1 \cdot r^2 = -r^2
\]
\[
-1 \cdot (-2r) = 2r
\]
\[
-1 \cdot 3 = -3
\]

So, the result of this part is:
\[
-r^2 + 2r - 3
\]

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

4. Combine like terms:
- \(r^3\) is alone.
- Combine the \(r^2\) terms: \(-2r^2 - r^2 = -3r^2\).
- Combine the \(r\) terms: \(3r + 2r = 5r\).
- Constant term: \(-3\).

Putting it all together, the final expression is:
\[
r^3 - 3r^2 + 5r - 3
\]

So, the result of multiplying \((r - 1)(r^2 - 2r + 3)\) is:
\[
\boxed{r^3 - 3r^2 + 5r - 3}
\]