simplify (a²+a√2+1)(a²-a√2+1)
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( a^2 + a√2 + 1 ) ( a^2 - a√2 + 1 ).
={a^2 + (a√2 + 1 ) } {a^2 - ( a√2 + 1 ) }
use identity :
(a + b ) ( a - b ) = a^2 - b^2 , we get
=( a^2 )^2 - ( a√2+ 1 )^2
=a^4 - ( 2a^2 + 2√2a + 1 )
=a^4 - 2a^2 - 2√2 a - 1
=a^4 - 2a( a + √2 ) - 1
_______________________________
|| hope helps || _______________________________
={a^2 + (a√2 + 1 ) } {a^2 - ( a√2 + 1 ) }
use identity :
(a + b ) ( a - b ) = a^2 - b^2 , we get
=( a^2 )^2 - ( a√2+ 1 )^2
=a^4 - ( 2a^2 + 2√2a + 1 )
=a^4 - 2a^2 - 2√2 a - 1
=a^4 - 2a( a + √2 ) - 1
_______________________________
|| hope helps || _______________________________
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