Factorize
Factorize x 4 + 6 4 .
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2 solutions
did the same
x 4 + 6 4 x 4 + 1 6 x 2 + 6 4 − 1 6 x 2 ( x 4 + 1 6 x 2 + 6 4 ) − ( 1 6 x 2 ) ( x 2 + 8 ) 2 − ( 4 x ) 2 ( x 2 + 8 + 4 x ) ( x 2 + 8 − 4 x ) ( x 2 + 4 x + 8 ) ( x 2 − 4 x + 8 )
We rewrite x 4 + 6 4 as ( x ) 4 + 4 ( 2 ) 4 which is a similar form of Sophie Germain identity which states that a 4 + 4 b 4 = ( a 2 + 2 a b + 2 b 2 ) ( a 2 − 2 a b + 2 b 2 ) .Thus we have:
( x ) 4 + 4 ( 2 ) 4 = ( x 2 + 4 x + 8 ) ( x 2 − 4 x + 8 )