Question 147000
For this problem use the FOIL method and an example problem,
{{{(A+B)(C+D)}}}
First:{{{(highlight(A)+B)(highlight(C)+D):A*C}}}
Outer:{{{(highlight(A)+B)(C+highlight(D)):A*D}}}
Inner:{{{(A+highlight(B))(highlight(C)+D):B*C}}}
Last:{{{(A+highlight(B))(C+highlight(D)):B*D}}}
Then add them all together.
{{{(A+B)(C+D)= A*C+A*D+B*C+B*D}}}
Then add them all together.
{{{(8*sqrt(6)+3*sqrt(2))*(4*sqrt(6)-5*sqrt(2))}}}
First:{{{(8*sqrt(6))*(4*sqrt(6))=8*4*6=192}}}
Outer:{{{(8*sqrt(6))*(-5*sqrt(2))=-40*sqrt(12)}}}
Inner:{{{(3*sqrt(2))*(4*sqrt(6))=12*sqrt(12)}}}
Last:{{{(3*sqrt(2))*(-5*sqrt(2))=3*(-5)*2=-30}}}
Now add it all together,
{{{(8*sqrt(6)+3*sqrt(2))*(4*sqrt(6)-5*sqrt(2))=192-40*sqrt(12)+12*sqrt(12)-30}}}
{{{(8*sqrt(6)+3*sqrt(2))*(4*sqrt(6)-5*sqrt(2))=162-28*sqrt(12)}}}
Further simplification is possible,
{{{sqrt(12)=sqrt(4*3)=2*sqrt(3)}}}
{{{(8*sqrt(6)+3*sqrt(2))*(4*sqrt(6)-5*sqrt(2))=162-56*sqrt(3)}}}