Упростите выражение (a-8+32a/(a-8))(8+a-32a/(8+a)).

\[\left( a - 8 + \frac{32a}{a - 8} \right)\left( 8 + a - \frac{32a}{8 + a} \right) =\]

\[= \frac{(a - 8)(a - 8) + 32a}{a - 8} \cdot\]

\[\cdot \frac{(8 + a)(8 + a) - 32a}{8 + a} =\]

\[= \frac{a^{2} - 16a + 64 + 32a}{a - 8} \cdot\]

\[\cdot \frac{64 + 16a + a^{2} - 32a}{8 + a} = \frac{a^{2} + 16a + 64}{a - 8} \cdot\]

\[\cdot \frac{a^{2} - 16a + 64}{8 + a} = \frac{(a + 8)^{2}(a - 8)^{2}}{(a - 8)(a + 8)} =\]

\[= (a + 8)(a - 8) = a^{2} - 64\]