Multiply the polynomials (2r−5)(r+4) . _r2+_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).

1. Multiply the first terms: $$2r\cdot r=2r^2$$

2. Multiply the outer terms: $$2r\cdot 4=8r$$

3. Multiply the inner terms: $$-5\cdot r=-5r$$

4. Multiply the last terms: $$-5\cdot 4=-20$$

Now, we can combine all these results: $$2r^2+8r-5r-20$$

Combine like terms: $$2r^2+(8r-5r)-20=2r^2+3r-20$$

So, the resulting polynomial is: $$\boxed{{\displaystyle 2r^2+3r-20}}$$