Example 2. Factorize in the set of real numbers $R$:
$$
a^{4}-14 a^{2}+25
$$
\begin{array}{l}\text { Sol } \text { Original expression }=\left(a^{4}-10 a^{2}+25\right)-4 a^{2} \\ =\left(a^{2}-5\right)^{2}-(2 a)^{2}=\left(a^{2}+2 a-5\right) \\ -\cdot\left(a^{2}-2 a-5\right)=(a+1+\sqrt{6})(a+1 \\ -\sqrt{6})(a-1+\sqrt{6})(a-1-\overline{\sqrt{6}}) .\end{array}