Question

用平方差公式计算（2+1）（2的2次方+1）（2的4次方+1）（2的8次方+1）-2的16次方

Answer 1

(2+1)(2^2+1)(2^4+1)(2^8+1)-2^16

=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)-2^16

=(2^2-1)(2^2+1)(2^4+1)(2^8+1)-2^16

=(2^4-1)(2^4+1)(2^8+1)-2^16

=(2^8-1)(2^8+1)-2^16

=2^16-1-2^16

=-1

提示：在前面加2-1,再反复用平方差公式.