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