Find the following product:
$(x^{2}-1)(x^{4}+x^{2}+1)$
$(x^{2}-1)(x^{4}+x^{2}+1)$
$(X^6-1)$ We use the algebraic identity $(a-b)(a^{2}+ab+b^{2}) = a^{3}-b^{3}$.
Given expression: $(x^{2}-1)(x^{4}+x^{2}+1)$
Rewrite the expression as: $(x^{2}-1)((x^{2})^{2} + (x^{2})(1) + (1)^{2})$
Here,$a = x^{2}$ and $b = 1$.
Applying the identity: $(x^{2})^{3} - (1)^{3}$
$= x^{6} - 1$
Given expression: $(x^{2}-1)(x^{4}+x^{2}+1)$
Rewrite the expression as: $(x^{2}-1)((x^{2})^{2} + (x^{2})(1) + (1)^{2})$
Here,$a = x^{2}$ and $b = 1$.
Applying the identity: $(x^{2})^{3} - (1)^{3}$
$= x^{6} - 1$
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