(0.1+0.21+0.31)*(0.21+0.31+0.41)-(0.1+0.21+0.31+0.41)*(0.21+0.31)的简便计算

答：设0.1+0.21+0.31=a,0.21+0.31=b.则：a-b=0.1(0.1+0.21+0.31)× (0.21+0.31+0.41)-(0.1+0.21+0.31+0.41)×(0.21+0.31)=a(b+0.41)-(a+0.41)b=ab+0.41a-ab-0.41b=0.41(a-b)因为：a-b=0.1所以：原式=0.41×0.1=0.041...