Question

39*41=40^2-1^2 48*52=50^2-2^2 .m*n=?

Answer 1

m*n=[(m+n)/2 ]^2 - [(m-n)/2 ]^2

m*n=1/4 [(m+n)^2-(m-n)^2]

这其实是个恒等式

m*n=1/4 [(m+n)^2-(m-n)^2]

＝1/4 [ (m^2+n^2+2mn)-(m^2+n^2-2mn)]

=1/4 (4mn)

=mn

只是利用了变形,使计算简便而已