Question

multiply the polynomials (2r - 5)(r + 4) using this template
_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).

1. First, multiply \( 2r \) by \( r \):
\[
2r \cdot r = 2r^2
\]

2. Next, multiply \( 2r \) by \( 4 \):
\[
2r \cdot 4 = 8r
\]

3. Now, multiply \( -5 \) by \( r \):
\[
-5 \cdot r = -5r
\]

4. Lastly, multiply \( -5 \) by \( 4 \):
\[
-5 \cdot 4 = -20
\]

Now, we combine all these results:
\[
2r^2 + 8r - 5r - 20
\]

Combine like terms (\( 8r - 5r \)):
\[
2r^2 + 3r - 20
\]

So, the final result is:
\[
\boxed{2r^2 + 3r - 20}
\]

In the template format you provided, it would be:
\[
2r^2 + 3r - 20
\]
Where the coefficients are:
- \( _ = 2 \) (for \( r^2 \))
- \( _ = 3 \) (for \( r \))
- \( _ = -20 \) (constant)