Find the following products:$ \left(x^{3}+1\right)\left(x^{6}-x^{3}+1\right) $

Given: 

\( \left(x^{3}+1\right)\left(x^{6}-x^{3}+1\right) \)

To do: 

We have to find the given product.

Solution: 

We know that,

$a^{3}+b^{3}=(a+b)(a^{2}-a b+b^{2})$

$a^{3}-b^{3}=(a-b)(a^{2}+a b+b^{2})$

Therefore,

$(x^{3}+1)(x^{6}-x^{3}+1)=(x^{3}+1)[(x^{3})^{2}-x^{3} \times 1+(1)^{2}]$

$=(x^{3})^{3}+(1)^{3}$

$=x^{9}+1$

 Hence, $(x^{3}+1)(x^{6}-x^{3}+1)=x^{9}+1$.

Tutorialspoint

Updated on: 10-Oct-2022

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