I've got an assignment that requires me to create algebraic rules for +* - / of three and four digit numbers.

For example, three digit subtraction could be expressed as:

100h + 10t + u - (100u + 10t + t), where we take a random three digits, and subtract the reversed sequence. This reduces to 99 ( h - u ), which is quite neat.

I've run into muddy puddles when trying to multiply and divide three and four digit sequences and their inverses/reverses ( I think its because I don't understand factorising ). For example, for a multiplication of 100h + 10t + u * (100u + 10t + h) , my best effort is 10001hu + 1010tu + 1010th + 100(h + t + u all squared). Even my nascent mathematical appreciation tells me this lacks a certain elegance.

Any suggestions please ?