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

Question

.(2 points)
r3+
r2+
r+

Answer 1

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

We will multiply each term in the first polynomial by each term in the second polynomial:

\[ (r - 1)(r^2 - 2r + 3) \]

1. Distributing \(r\): \[ r \cdot r^2 = r^3 \] \[ r \cdot (-2r) = -2r^2 \] \[ r \cdot 3 = 3r \]

2. Distributing \(-1\): \[ -1 \cdot r^2 = -r^2 \] \[ -1 \cdot (-2r) = 2r \] \[ -1 \cdot 3 = -3 \]

Now, we combine all of these results: \[ r^3 - 2r^2 + 3r - r^2 + 2r - 3 \]

Next, we combine like terms:

1. \(r^3\) remains as is.
2. For the \(r^2\) terms: \(-2r^2 - r^2 = -3r^2\)
3. For the \(r\) terms: \(3r + 2r = 5r\)
4. The constant term: \(-3\)

Putting it all together, we get: \[ r^3 - 3r^2 + 5r - 3 \]

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

You can fill in the blanks as follows:

• \(r^3\)
• \(-3r^2\)
• \(5r\)
• \(-3\)