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Question
Find the following product:
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Solution
Given `(x^2 - 1) (x^4+x^2 + 1)`
We shall use the identity `(a-b) (a^2 + ab + b^2) = a^3 - b^3`
We can rearrange the `(x^2 - 1)(x^4 + x^2 + 1)`as
\[\left( x^2 - 1 \right)\left[ \left( x^2 \right)^2 + \left( x^2 \right)\left( 1 \right) + \left( 1 \right)^2 \right]\]
`= (x^2)^3 - (1)^3`
` = (x^2) xx(x^2) xx (x^2) - (1) xx (1) xx (1)`
` = x^6 - 1^3`
` = x^6 - 1`
Hence the Product value of `(x^2 - 1) (x^4 +x^2 + 1)`is `x^6 - 1`.
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