Question 352223
{{{(3*sqrt(2)-9*sqrt(6))*(5*sqrt(2)+15*sqrt(6))}}}
ok, in order to simplify this problem we use distributive property
{{{(a-b)(c+d)=ac+ad-bc-bd}}}
{{{3*sqrt(2)*5*sqrt(2)+3*sqrt(2)*15*sqrt(6)-9*sqrt(6)*5*sqrt(2)-9*sqrt(6)*15*sqrt(6))}}} now you simplify


{{{15*sqrt(2)*sqrt(2)+45*sqrt(2)*sqrt(6)-45*sqrt(6)*sqrt(2)-135*sqrt(6)*sqrt(6))}}} simplify further, for example {{{sqrt(2)*sqrt(2)=sqrt(2*2)=sqrt(4)=2}}}, so we have

{{{15*2+45*sqrt(12)-45*sqrt(12)-135*6)}}} 


{{{30+45*sqrt(12)-45*sqrt(12)-810)}}} Notice that the two terms in the middle are the same with opposite signs so they add to zero, thus you get

{{{30-810=-780}}}