32 x 5 − 2 x = 2 x ( 16 x 4 − 1 ) = 2 x u se : a 2 − b 2 = ( a − b ) ( a + b ) [ ( 4 x 2 ) 2 − 1 2 ] = 2 x ( 4 x 2 − 1 ) ( 4 x 2 + 1 ) = 2 x u se : a 2 − b 2 = ( a − b ) ( a + b ) [ ( 2 x ) 2 − 1 2 ] ( 4 x 2 + 1 ) \center = 2 x ( 2 x − 1 ) ( 2 x + 1 ) ( 4 x 2 + 1 )
To completely factor 32 x 5 − 2 x , first factor out the GCF of 2 x , resulting in 2 x ( 16 x 4 − 1 ) . Then apply the difference of squares formula to factor further into 2 x ( 2 x − 1 ) ( 2 x + 1 ) ( 4 x 2 + 1 ) . The final answer is 2 x ( 2 x − 1 ) ( 2 x + 1 ) ( 4 x 2 + 1 ) .
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