Question 809711
{{{((2/3)+sqrt(2))((3/4)-2(sqrt(2)))}}}
use FOIL(First Outer Inner Last) Method
{{{((2/3)(3/4)) + ((2/3)(-2(sqrt(2)))) + ((3/4)(sqrt(2))) + ((sqrt(2))(-2(sqrt(2^2))))}}}
{{{(1/2)+((-4sqrt(2))/3)+(3(sqrt(2))/4)-4}}}

now if u need it all over the common denom which is simply multiplying everything by the common 1/1 = ((1*2*3*4)/(1*2*3*4)) = 24/24
writing this out is a lot more work then doing this in my head...i suggest u memorize the process and do it in your head its way faster.

{{{((1/2)((1*2*3*4)/(1*2*3*4))) + (((-4sqrt(2))/3)((1*2*3*4)/(1*2*3*4))) + ((3(sqrt(2))/4)((1*2*3*4)/(1*2*3*4))) + ((-4)((1*2*3*4)/(1*2*3*4)))}}}
below shows cross outs
{{{((1/cross(2))((1*cross(2)*3*4)/(1*2*3*4))) + (((-4sqrt(2))/cross(3))((1*2*cross(3)*4)/(1*2*3*4))) + ((3(sqrt(2))/cross(4))((1*2*3*cross(4))/(1*2*3*4))) + ((-4)((24)/(24)))}}}
multiplied outcome:
{{{(12/24) + ((-32sqrt(2))/24) + ((18sqrt(2))/24) - (96/24)}}}
{{{highlight_green((-84-18sqrt(2))/24)}}}
this was a pain to code in here hope this is clear enough.