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

1.	Factorize each of the following algebraic expressions :`x^8-y^8`(ii) `a^(12)x^4-a^4x^(12)`
Answer» We have `(x^8-y^8) =(x^4)-(y^4)^2` `=(x^4-y^4)(x^4+y^4)` `={(x^2)^2-(y^2)^2}(x^4+y^4+2x^2y^2-2x^2y^2)`. `=(x^2-y^2)(x^2+y^2)[(x^2+y^2)^2-(sqrt(2)xy)^2]` `=(x-y)(x+y)(x^2+y^2) (x^2+y^2-sqrt(2)xy)(x^2+y^2+qrt(2)xy)`. `therefore (x^8-y^8)=(x-y)(x+y)(x^2+y^2)(x^2+y^2-x sqrt(2)xy)(x^2+y^2+sqrt(2)xy)`.

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