Question

Вычислите рациональным способом.
32*31-31*30+30*29-29*28+28*27-27*26+26*25-25*24+24*23-23*22=

Answer 1

31*(32-30)+29*(30-28)+27*(28-26)+25*(26-24)+23*(24-22)=2*(31+29+27+25+23)=2*135=270

Answer 2

$32*31-31*30+30*29-29*28+ \ +28*27-27*26+26*25-25*24+ 24*23-23*22= \ =31(32+30)+29(30-28)+27(28-26)+ \ +25(26-24)+23(24-22)=31*2+29*2+27*2+ \ +25*2+23*2=2(31+29+27+25+23)= \ =2*135=270$