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

Answer 1

To multiply the two polynomials (r-1)(r^2-2r+3), we can use the distributive property.

First, we distribute r from the first term (r-1) to each term in the second polynomial (r^2-2r+3):

(r-1)(r^2-2r+3) = r(r^2-2r+3) - 1(r^2-2r+3)

Simplifying each term:

= r^3 - 2r^2 + 3r - r^2 + 2r - 3

Combining like terms:

= r^3 - 3r^2 + 5r - 3

Thus, the simplified polynomial expression is r^3 - 3r^2 + 5r - 3.