Multiply to simplify the polynomial expression (r−1)(r^2−2r+3).
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.
To simplify the polynomial expression (r-1)(r^2-2r+3), we can use the distributive property of multiplication.
First, let's distribute the multiplication to the terms inside the parentheses:
(r-1)(r^2-2r+3) = r(r^2-2r+3) - 1(r^2-2r+3)
Now, we multiply each term inside the parentheses by the term outside the parentheses:
r(r^2-2r+3) - 1(r^2-2r+3) = r * r^2 + r * (-2r) + r * 3 - 1 * r^2 - 1 * (-2r) - 1 * 3
Simplifying further, we get:
r^3 - 2r^2 + 3r - r^2 + 2r - 3
Finally, we combine like terms:
r^3 - 3r^2 + 5r - 3
So, the simplified form of (r-1)(r^2-2r+3) is r^3 - 3r^2 + 5r - 3.