We use the FOIL technique: First Outside Inside Last $$\begin{aligned} \left({x^{7}-2}\right)\left({x^{7}+2}\right)&={x^{14}+2x^{7}-2x^{7}-4}\\ &={x^{14}-4} \end{aligned}$$ Alternatively, we might observe that this is the product of the sum and difference of two terms, in which case we may use the formula $$(a-b)(a+b)=a^2-b^2$$ and write $$\begin{aligned} \left({x^{7}-2}\right)\left({x^{7}+2}\right)&=\left(x^{7}\right)^2-2^2\\ &={x^{14}-4} \end{aligned}$$ which is the same result we obtained using the FOIL method.