Question

(m+n)² (m-n)² (m² +n² )²

还有个：（2+1）（2²+1）（2四次+1）······（2的2012次+1）的个位是什么？（刚刚问错了）

Answer 1

(m+n)²(m-n)²(m² +n² )²
=(m+n)(m-n)(m+n)(m-n)(m²+n²)(m²+n²)
=(m²-n²)(m²+n²)(m²-n²)(m²+n²)
=(m^4-n^4)²
=m^8-2m^4n^4+n^8
(2+1)(2²+1)(2^4+1)······(2^2012+1)
=(2-1)(2+1)(2²+1)(2^4+1)······(2^2012+1)
=(2²-1)(2²+1)(2^4+1)······(2^2012+1)
=(2^4-1)(2^4+1)······(2^2012+1)
=(2^2012-1)(2^2012+1)
=2^4024-1

Answer 2

(m+n)² (m-n)² (m² +n² )²

=[(m+n)(m-n)]² (m² +n² )²
=(m² -n²)² (m² +n² )²
=(m^4-n^4)²

(2+1)(2²+1)(2^4+1)······(2^2012+1)

=(2-1)(2+1)(2²+1)(2^4+1)······(2^2012+1)
=(2²-1)(2²+1)(2^4+1)······(2^2012+1)
=(2^2012-1)(2^2012+1)
=2^4024-1