Multiply to simplify the polynomial expression (r−1)(r2−2r+3)
.(2 points)
r3+
r2+
r+
To simplify the polynomial expression (r−1)(r^2−2r+3), we multiply each term in the first polynomial by each term in the second polynomial. Let's go through the multiplication term by term:
(r * r^2) = r^3
(r * -2r) = -2r^2
(r * 3) = 3r
(-1 * r^2) = -r^2
(-1 * -2r) = 2r
(-1 * 3) = -3
Now we combine like terms:
r^3 + (-2r^2) + 3r + (-r^2) + 2r + (-3)
Combine the r^2 terms and the r terms:
r^3 + (-2r^2 - r^2) + (3r + 2r) - 3
r^3 - 3r^2 + 5r - 3
Therefore, the simplified polynomial expression is:
r^3 - 3r^2 + 5r - 3