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

##### 1 Answer

#### Answer:

#### 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#