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Question
Factorize each of the following expression:
x8 − 1
Solution
\[x^8 - 1\]
\[ = ( x^4 )^2 - 1^2 \]
\[ = ( x^4 - 1)( x^4 + 1)\]
\[ = [( x^2 )^2 - 1^2 ]( x^4 + 1)\]
\[ = ( x^2 - 1)( x^2 + 1)( x^4 + 1)\]
\[ = ( x^2 - 1^2 )( x^2 + 1)( x^4 + 1)\]
\[ = (x - 1)(x + 1)( x^2 + 1)( x^4 + 1)\]
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