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

Question

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Answer 1

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

1. Start by distributing \(r\) across the second polynomial:

   \[ r \cdot (r^2 - 2r + 3) = r^3 - 2r^2 + 3r \]

2. Next, distribute \(-1\) across the second polynomial:

   \[ -1 \cdot (r^2 - 2r + 3) = -r^2 + 2r - 3 \]

3. Now, combine the two results:

   \[ r^3 - 2r^2 + 3r - r^2 + 2r - 3 \]

4. Combine like terms:

   • For \(r^2\) terms: \(-2r^2 - r^2 = -3r^2\)
   • For \(r\) terms: \(3r + 2r = 5r\)
   • The constant term: \(-3\)

Putting it all together:

\[ r^3 - 3r^2 + 5r - 3 \]

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

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