Multiply to simplify the polynomial expression (r−1)(r2−2r+3).
To simplify the expression, we will use the distributive property to multiply the two binomials.
First, we multiply r by each term inside the second parentheses:
(r)(r^2) = r^3
(r)(-2r) = -2r^2
(r)(3) = 3r
Next, we multiply -1 by each term inside the second parentheses:
(-1)(r^2) = -r^2
(-1)(-2r) = 2r
(-1)(3) = -3
Combining like terms, we get:
r^3 - 2r^2 + 3r - r^2 + 2r - 3
Simplifying further, we get:
r^3 - 3r^2 + 5r - 3
So the simplified polynomial expression is r^3 - 3r^2 + 5r - 3.
To multiply the polynomials (r-1) and (r^2-2r+3), we will use the distributive property.
First, distribute the term r-1 to each term inside the second parentheses:
(r-1)(r^2-2r+3) = r(r^2-2r+3) - 1(r^2-2r+3)
Now, distribute each term inside the first parentheses:
= r(r^2) - r(2r) + r(3) - 1(r^2) + 1(2r) - 1(3)
Simplify each term:
= r^3 - 2r^2 + 3r - r^2 + 2r - 3
Combine like terms:
= r^3 - 3r^2 + 5r - 3
So, the simplified polynomial expression is r^3 - 3r^2 + 5r - 3.