Solve $(x^{2} - x + 1) (x^{4} + x^{3} + x + 1)$ .

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Solution

$(x^{2} - x + 1) (x^{4} + x^{3} + x + 1)$

$= x^{2} (x^{4} + x^{3} + x + 1) - x (x^{4} + x^{3} + x + 1) + 1 (x^{4} + x^{3} + x + 1)$

$= x^{6} + x^{5} + x^{3} + x^{2} - x^{5} - x^{4} - x^{2} - x + x^{4} + x^{3} + x + 1$

$= x^{6} + 2 x^{3} + 1$ (Ans)

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