Question

How do you multiply `(2r+9s)^2`?

Answer 1

`4r^2+36rs+81s^2`

Explanation:

Consider `(2r+9s)^2=(2r+9s)(2r+9s)`

We must ensure that each term in the 2nd bracket is multiplied by each term in the first bracket.This can be achieved as follows.

`(color(red)(2r+9s))(2r+9s)`

`=color(red)(2r)(2r+9s)+color(red)(9s)(2r+9s)`

distribute the brackets : `4r^2+18rs+18rs+81s^2`

and simplifying to obtain : `4r^2+36rs+81s^2`

`rArr(2r+9s)^2=4r^2+36rs+81s^2`
`"----------------------------------------------------------"`
Alternatively there is the FOIL method.

`Fto" First terms"`
`Oto" Outer terms"`
`Ito" Inner terms"`
`Lto" Last terms"`

F-multiply the first terms in each bracket together.
O-multiply the outer terms together.
I-multiply the inner terms together.
L-multiply the last terms together.

`rArr(2r+9s)(2r+9s)`

`=(2rxx2r)+(2rxx9s)+(2rxx9s)+(9sxx9s)`

`=4r^2+18rs+18rs+81s^2=4r^2+36rs+81s^2`