Question

Multiply the polynomials (2r−5)(r+4)
(
2
𝑟
−
5
)
(
𝑟
+
4
)
.(2 points)
r2+
𝑟
2
+
r+
𝑟
+

Answer 1

To multiply the polynomials \((2r - 5)(r + 4)\), we will use the distributive property (also known as the FOIL method for binomials):

1. **First:** Multiply the first terms:
\[
2r \cdot r = 2r^2
\]

2. **Outer:** Multiply the outer terms:
\[
2r \cdot 4 = 8r
\]

3. **Inner:** Multiply the inner terms:
\[
-5 \cdot r = -5r
\]

4. **Last:** Multiply the last terms:
\[
-5 \cdot 4 = -20
\]

Now, combine all these results:
\[
2r^2 + 8r - 5r - 20
\]

Combine the like terms \(8r\) and \(-5r\):
\[
2r^2 + (8r - 5r) - 20 = 2r^2 + 3r - 20
\]

Thus, the product of the polynomials \((2r - 5)(r + 4)\) is:
\[
\boxed{2r^2 + 3r - 20}
\]