The expressions $A$ = $1 \times 2 + 3 \times 4 + 5 \times 6 + \cdots + 37 \times 38 + 39$ and $B$ = $1 + 2 \times 3 + 4 \times 5 + \cdots + 36 \times 37 + 38 \times 39$ are obtained by writing multiplication and addition operators in an alternating pattern between successive integers.  Find the positive difference between integers $A$ and $B$.
We have \[|A-B|=|1+3(4-2)+5(6-4)+ \cdots + 37(38-36)-39(1-38)|\]\[\implies |2(1+3+5+7+ \cdots +37)-1-39(37)|\]\[\implies |361(2)-1-39(37)|=|722-1-1443|=|-722|\implies \boxed{722}\]