Solve the following:
$(p + q) (p - q) (p^{2} + q^{2}) (p^{4} + q^{4}) (p^{8} + q^{8})$

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Solution

$\begin{matrix} (p + q) (p - q) (p^{2} + q^{2}) (p^{4} + q^{4}) (p^{8} + q^{8}) \Rightarrow (p^{2} - q^{2}) (p^{2} + q^{2}) (p^{4} + q^{4}) (p^{8} + q^{8}) \Rightarrow (p^{4} - q^{4}) (p^{4} + q^{4}) (p^{8} + q^{8}) \Rightarrow (p^{8} - q^{8}) (p^{8} + q^{8}) [a^{2} - b^{2} = (a - b) (a + b)] (p^{16} - q^{16}) A n s . \end{matrix}$

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