Question

Multiply to simplify the polynomial expression (r−1)(r2−2r+3)
.

Answer 1

Simplify the polynomial expression (xy−2)(x2+1)
.(2 points)
__x3y+_x2+_xy+_

Answer 2

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

1. Multiply \(r\) by each term in \(r^2 - 2r + 3\):
- \(r \cdot r^2 = r^3\)
- \(r \cdot (-2r) = -2r^2\)
- \(r \cdot 3 = 3r\)

So, combining these, we have:
\[
r^3 - 2r^2 + 3r
\]

2. Now multiply \(-1\) by each term in \(r^2 - 2r + 3\):
- \(-1 \cdot r^2 = -r^2\)
- \(-1 \cdot (-2r) = 2r\)
- \(-1 \cdot 3 = -3\)

So, combining these, we have:
\[
-r^2 + 2r - 3
\]

3. Now, combine all the terms from step 1 and step 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: \(3r + 2r = 5r\)

So, we have:
\[
r^3 - 3r^2 + 5r - 3
\]

The simplified polynomial expression is:
\[
\boxed{r^3 - 3r^2 + 5r - 3}
\]