Question

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

Answer 1

To simplify the polynomial expression \((r - 1)(r^2 - 2r + 3)\), we can use the distributive property (also known as the FOIL method for binomials). We will distribute \( (r - 1) \) across each term in \( (r^2 - 2r + 3) \).

1. Distribute \( r \):
\[
r \cdot r^2 = r^3
\]
\[
r \cdot (-2r) = -2r^2
\]
\[
r \cdot 3 = 3r
\]

2. Distribute \(-1\):
\[
-1 \cdot r^2 = -r^2
\]
\[
-1 \cdot (-2r) = 2r
\]
\[
-1 \cdot 3 = -3
\]

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

Next, we can combine like terms:
- The \( -2r^2 \) and \( -r^2 \) combine to give \( -3r^2 \).
- The \( 3r \) and \( 2r \) combine to give \( 5r \).

Thus, the simplified expression is:
\[
r^3 - 3r^2 + 5r - 3
\]

So, the final answer is:
\[
\boxed{r^3 - 3r^2 + 5r - 3}
\]