In Example 1, think of it like this :

(a - b) * c .

Then the algorithm performs these operations :

[(a-b) + 10]*c + 100 -10*c - 100

which is

a*c - b*c + 10*c + 100 - 10*c - 100 .

equals

a*c - b*c

equals

(a - b) * c which is the original equation.

 

In Example 2, write it as :

a * b .

The algorithm does these operations.

(a + 100) * b + 10000 - 100*b - 10000.

This is the same as :

a * b + 100 * b + 10000 - 100 * b - 10000

equals

a * b which is the original equation.

 

Gary Flom
Atlanta, Ga
USA