The product of $(x^{2} - 1) (x^{4} + x^{2} + 1)$ is equal to

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Solution

$(x^{2} - 1) (x^{4} + x^{2} + 1)$
$(x^{2} - 1) [(x^{2})^{2} + x^{2} \times 1 + (1)^{2}]$
${Using identity (a^{3} - b^{3}) = (a - b) (a^{2} + a b + b^{2})}$
$= [(x^{2})^{3} - (1)^{3}]$
$= (x^{6} - 1)$

Hence, $(c)$ is the correct option.

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