Question

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

Answer 1

To multiply the polynomials \( (2r - 5)(r + 4) \), we can 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 \( -5r \):
\[
2r^2 + (8r - 5r) - 20 = 2r^2 + 3r - 20
\]

So, the final result of multiplying the polynomials is:
\[
\boxed{2r^2 + 3r - 20}
\]