Question

Factorise : a⁶ - 7a³ - 8

Answer 1

We know that,
a³ + b³ = ( a + b )( a² - ab + b² )                     ....(1)
a³ - b³ = ( a - b )( a² + ab + b² )                      ....(2)
a⁶ - 7a³ - 8
= a⁶ - 8a³ + a³ - 8
= a³( a³ - 8) + 1( a³ - 8 )
= ( a³ + 1 )( a³ - 8 )
= ( a³ + 1³ )( a³ - 2³ )
= ( a + 1 )( a² - a + 1 )( a - 2 )( a² + 2a + 4 )       
[ From(1) and (2) ]
= ( a + 1 )( a - 2)( a² - a + 1 )( a² + 2a + 4 )