How do you simplify #(3 - 2sqrt2) (2 - 5sqrt2)#?

1 Answer
Feb 27, 2018

Answer:

#26-19sqrt(2)#

Explanation:

Use the F.O.I.L. method:

F irsts
O utsides
I nsides
L asts

Where each of the above terms listed are multiplied and added up/simplified at the end.

Firsts:
#3*2=6#
Outsides:
#3*(-5sqrt(2))=(3)(-5)sqrt(2)=-15sqrt(2)#
Insides:
#-2sqrt(2)*2=(-2)(2)sqrt(2)=-4sqrt(2)#

Lasts:
#-2sqrt(2)*-5sqrt(2)=(-2)(-5)(sqrt(2)^2)=10(2)=20# (Because #sqrt(a)^2=a#)

Add all of these together:
#6-15sqrt(2)-4sqrt(2)+20#

Combine like terms:

#6+20-4sqrt(2)-15sqrt(2)=26-19sqrt(2)#