Question

Multiply the polynomial expression (x+2)(x−4)
.(2 points)

Answer 1

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

Answer 2

To multiply the polynomial expression \((x + 2)(x - 4)\), we can use the distributive property (also known as the FOIL method for binomials).

1. **First**: Multiply the first terms:
\(x \cdot x = x^2\)

2. **Outer**: Multiply the outer terms:
\(x \cdot (-4) = -4x\)

3. **Inner**: Multiply the inner terms:
\(2 \cdot x = 2x\)

4. **Last**: Multiply the last terms:
\(2 \cdot (-4) = -8\)

Now, combine all these results:
\[
x^2 - 4x + 2x - 8
\]

Combine the like terms \(-4x\) and \(2x\):
\[
x^2 - 2x - 8
\]

Thus, the product of the polynomial expression \((x + 2)(x - 4)\) is:
\[
\boxed{x^2 - 2x - 8}
\]

Answer 3

To multiply and simplify the polynomial expression \((r - 1)(r^2 - 2r + 3)\), we can use the distributive property.

1. **Distribute \(r\) to each term in the second polynomial**:
\[
r \cdot r^2 = r^3
\]
\[
r \cdot (-2r) = -2r^2
\]
\[
r \cdot 3 = 3r
\]

2. **Distribute \(-1\) to each term in the second polynomial**:
\[
-1 \cdot r^2 = -r^2
\]
\[
-1 \cdot (-2r) = 2r
\]
\[
-1 \cdot 3 = -3
\]

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

4. **Combine like terms**:
- Combine \( -2r^2 \) and \( -r^2 \):
\(-2r^2 - r^2 = -3r^2\)

- Combine \( 3r \) and \( 2r \):
\(3r + 2r = 5r\)

So, the expression becomes:
\[
r^3 - 3r^2 + 5r - 3
\]

Thus, the simplified product of the polynomial expression \((r - 1)(r^2 - 2r + 3)\) is:
\[
\boxed{r^3 - 3r^2 + 5r - 3}
\]