Question

Multiply to simplify the polynomial expression (r−1)(r^2−2r+3) .(2 points)
r^3+r^2+r+

Answer 1

To simplify 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 the second polynomial:
\[
r \cdot (r^2) = r^3,
\]
\[
r \cdot (-2r) = -2r^2,
\]
\[
r \cdot (3) = 3r.
\]

2. Next, distribute \(-1\) to each term in the second polynomial:
\[
-1 \cdot (r^2) = -r^2,
\]
\[
-1 \cdot (-2r) = 2r,
\]
\[
-1 \cdot (3) = -3.
\]

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

4. Combine like terms:
- For \( r^2 \):
\[
-2r^2 - r^2 = -3r^2,
\]
- For \( r \):
\[
3r + 2r = 5r.
\]

5. Putting this all together:
\[
r^3 - 3r^2 + 5r - 3.
\]

So, the simplified form of \((r - 1)(r^2 - 2r + 3)\) is:

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