Factorise $\left(a^{6}-b^{6}\right)$.
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Factorise $\left(a^{6}-b^{6}\right)$.
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Solution—

We have

$$

\begin{aligned}

&\left(a^{6}-b^{6}\right) \\

=&\left(a^{3}\right)^{2}-\left(b^{3}\right)^{2} \\

=&\left(a^{3}-b^{3}\right)\left(a^{3}+b^{3}\right) \\

=&(a-b)\left(a^{2}+a b+b^{2}\right)(a+b)\left(a^{2}-a b+b^{2}\right) \\

=&(a-b)(a+b)\left(a^{2}+a b+b^{2}\right)\left(a^{2}-a b+b^{2}\right) . \\

\therefore \quad &\left(a^{6}-b^{6}\right)=(a-b)(a+b)\left(a^{2}+a b+b^{2}\right)\left(a^{2}-a b+b^{2}\right) .

\end{aligned}

$$

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