Question

Multiply the polynomials (2r-5) (r+4)

Answer 1

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

Here's how it works step-by-step:

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

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 in each binomial.
\[
-5 \cdot 4 = -20
\]

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:
\[
\boxed{2r^2 + 3r - 20}
\]