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Question
Find the following product:
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Solution
Given (x3 + 1) (x6 − x3 + 1)
We shall use the identity, `a^3 + b^3 = (a+ b) (a^2 + b^2 - ab)`
We can rearrange the `(x^3 + 1) (x^6 - x^3 + 1)`as
`= (x^3 + 1) [(x^3)^2 - (x^3)(1) + (1)^2]`
`= (x^3)^3 + (1)^3`
` = (x^3) xx (x^3)xx (x^3) + (1) xx (1) xx (1) `
` = x^9 + 1^3`
` = x^9 + 1`
Hence the Product value of `(x^3 + 1) (x^6 - x^3 + 1)`is .`x^9 + 1`.
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