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

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Answer 1 · 2018-02-27T14:45:23

$26-19sqrt(2)$

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:

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

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