I have an ordered pair $(ac+bd, ad+cb)$ where $a$, $b$, $c$ and $d$ are natural numbers. How can I rearrange that pair, so that exactly 3 multiplications, 3 additions and 1 subtraction are used?
I tried to place some of the factors outside the brackets for each component of the pair, but that always involves a division. I think that I have to add additional variables somehow, but I have no idea how to do that.
Can you give me a hint?