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Question
Mathematics
  1. ( 6 4 ) ( 2 6 + 8 ) (sqrt6-4)(2sqrt6+8)
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Answer: 20 6 -20sqrt6
Solution:
( 6 4 ) ( 2 6 + 8 ) (sqrt6-4)(2sqrt6+8)
= 6 2 6 + 6 8 4 2 6 4 8 =sqrt6*2sqrt6+sqrt6*8-4*2sqrt6-4*8 (distributive property of multiplication)
= 2 6 + 8 6 8 6 32 =2*6+8sqrt6-8sqrt6-32
= 12 32 =12-32
= 20 =-20
Therefore, ( 6 4 ) ( 2 6 + 8 ) = 20 (sqrt6-4)(2sqrt6+8)=-20. But if we assume that we need a numerical answer, we can simplify it further as:
( 6 4 ) ( 2 6 + 8 ) = 20 (sqrt6-4)(2sqrt6+8)=-20
= 20 6 6 6 =-20sqrt6*(sqrt6)/(sqrt6)
= 20 6 6 6 6 =-20sqrt6*(sqrt6*sqrt6)/(6)
= 20 6 36 6 =-20sqrt6*(sqrt36)/(6)
= 20 6 1 =-20sqrt6*1
= 20 6 =-20sqrt6
So, ( 6 4 ) ( 2 6 + 8 ) = 20 6 (sqrt6-4)(2sqrt6+8)=-20sqrt6.
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