若a=2,求3(a²+1)(a四次方+1)(a八次方+1)(a十六次方+1)

解
3(a²+1)(a^4+1)(a^8+1)(a^16+1)
=3(a²-1)(a²+1)(a^4+1)(a^8+1)(a^16+1)/(a²-1)
=3(a^4-1)(a^4+1)(a^8+1)(a^16+1)/(a²-1)
=3(a^8-1)(a^8+1)(a^16+1)/(a²-1)
=3(a^16-1)(a^16+1)/(a²-1)
=3(a^32-1)/(a²-1)
=3×(2^32-1)/(4-1)
=2^32-13×(2^32-1)/(4-1)怎么得到2^32-1的？就是将a=2代入=3×(2^32-1)/(2²-1)=3(2^32-1)/3=2^32-1