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Question
Factorise the following:
`x^8 - 1/x^8`
Sum
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Solution
Given `x^8 - 1/x^8`
We know that,
(a + b) (a – b) = a2 – b2
Hence,
⇒ `(x^4)^2 - (1/x^4)^2`
⇒ `(x^4 + 1/x^4) (x^4 - 1/x^4)`
⇒ `(x^4 + 1/x^4) (x^2 + 1/x^2) (x^2 - 1/x^2)`
⇒ `(x^4 + 1/x^4) (x^2 + 1/x^2) (x - 1/x) (x + 1/x)`
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