Question

(2r+s)(2r-s)
use box method

Answer 1

To use the box method, we draw a box and divide it into four equal sections, as shown below:

| 2r -s |
________|____________
2r | 4r^2 | -2rs |
- s | -2rs | s^2 |

In each section, we multiply the values on the corresponding sides. Then, we combine the like terms in each row and column.

Multiplying the values in each section:
1st section: (2r)(2r) = 4r^2
2nd section: (2r)(-s) = -2rs
3rd section: (-s)(2r) = -2rs
4th section: (-s)(-s) = s^2

Combining like terms in each row and column:
1st row: 4r^2 + (-2rs) = 4r^2 - 2rs
2nd row: -2rs + s^2 = -2rs + s^2

Therefore, the product of (2r+s) and (2r-s) is 4r^2 - 2rs - 2rs + s^2, which simplifies to 4r^2 - 4rs + s^2.