Factorize each of the following algebraic expressions : `x^8-y^8` (ii) `a^(12)x^4-a^4x^(12)`

Explanation

(i)`x^8-y^8`
`= (x^4+y^4) (x^4-y^4)`[ Using identity `a^2-b^2 = (a+b) (a-b)`]
`= (x^4+y^4) [(x^2)^2 - (y^2)^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)`

(ii) `a^(12)x^4-a^4x^(12)`
`=a^4x^4(a^8 - x^8)`
`=a^4x^4{(a^4)^2 - (x^4)^2}`
`=a^4x^4(a^4 + x^4) (a^4 - x^4`
`=a^4x^4(a^4 + x^4) {(a^2)^2 - (x^2)^2}`
`=a^4x^4(a^4 + x^4) (a^2 + x^2) (a^2 - x^2)`
`=a^4x^4(a^4 + x^4) (a^2 + x^2) {(a)^2 - (x)^2}`
`=a^4x^4(a^4 + x^4) (a^2 + x^2) (a + x) (a - x)`