(a-1)(a-3)(a+5)(a+7)+64
=[(a-1)(a+5)][(a-3)(a+7)]+64
=(a²+4a-5)(a²+4a-21)+64
=(a²+4a-5)[(a²+4a-5)-16]+64
=(a²+4a-5)²-16(a²+4a-5)+64
=(a²+4a-5-8)²
=(a²+4a-13)²
是完全平方数.