Question

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

Answer 1

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

1. Multiply \(r\) with each term in the second polynomial:
\[
r \cdot r^2 = r^3
\]
\[
r \cdot (-2r) = -2r^2
\]
\[
r \cdot 3 = 3r
\]

2. Now multiply \(-1\) with each term in the second polynomial:
\[
-1 \cdot r^2 = -r^2
\]
\[
-1 \cdot (-2r) = 2r
\]
\[
-1 \cdot 3 = -3
\]

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

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

Putting it all together, the simplified expression is:
\[
\boxed{r^3 - 3r^2 + 5r - 3}
\]