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

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).

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)