Multiply to simplify the polynomial expression (r−1)(r2−2r+3) .(2 points) r3+ r2+ r+

Answer 1

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

Let's distribute \(r - 1\) to each term in \(r^2 - 2r + 3\):

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, the result from this part is: \[ r^3 - 2r^2 + 3r \]

2. 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, the result from this part is: \[ -r^2 + 2r - 3 \]

Now, we combine all the terms together: \[ r^3 - 2r^2 + 3r - r^2 + 2r - 3 \]

Next, we combine like terms:

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

Now, putting it all together: \[ r^3 - 3r^2 + 5r - 3 \]

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