Factorise x {}^(8) - y {}^(8)

Question

Factorise
`x {}^(8) - y {}^(8)`

Answer 1

Solution :

`x {}^(8) - y {}^(8) = (x {}^(4) ) {}^(2) - (y {}^(4) ) {}^(2)`

`= (x {}^(4) + y {}^(4) )(x {}^(4) - y {}^(4) )`

`= (x {}^(4) + y {}^(4) )[(x {}^(2) ) {}^(2) - (y {}^(2) )]`

`= (x {}^(4) + y {}^(4) )(x {}^(2) + y {}^(2) )(x {}^(2) - y {}^(2) )`

`= (x {}^(4) + y {}^(4) )(x {}^(2) + y {}^(2) )(x + y)(x - y)`