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Let's try it on something really easy to be sure it works!

( 2 + 7 )( 8 + 3 ) = ( 9 )( 11 ) = 99

Now, with FOIL:

( 2 + 7 )( 8 + 3 ) = ( 2 )( 8 ) + ( 2 )( 3 ) + ( 7 )( 8 ) + ( 7 )( 3 ) = 16 + 6 + 56 + 21 = 99  Yep!


TRY IT:

Multiply this with FOIL, then check with the old, easy way:

( 4 + 6 )( 7 + 3 )


OK, now let's do it with some radicals:

( 7 - sqrt(2) )( 5 + sqrt(3) ) = ( 7 )( 5 ) + 7*sqrt(3) - 5*sqrt(2) - ( sqrt(2) )( sqrt(3) ) = 35 + 7*sqrt(3) - 5*sqrt(2) - sqrt(6)

We have to stop here since we can't combine anything!