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) to expand the expression:

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 terms: \[ 2r^2 + 8r - 5r - 20 \]

Next, combine like terms (\( 8r - 5r = 3r \)): \[ 2r^2 + 3r - 20 \]

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