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

Question

_r^2 + _r + _

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 you can do it step by step:

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 the results:

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

Combine like terms (\(8r - 5r\)):

\[ 2r^2 + 3r - 20 \]

So, the final result of multiplying the polynomials \((2r - 5)(r + 4)\) is:

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