Question

Multiply to simplify the polynomial expression r minus 1 times r squared minus 2R + 3

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

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

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

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

Now, putting everything together, we get:
\[
r^3 - 3r^2 + 5r - 3
\]

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