Is there any way to simplify the expression:
$$(a\pm b)(c\pm d)\quad ?$$ At first, I tried just distributing the values, and through FOIL I achieved:
$$ac \pm ad \pm bc \pm bd$$
This works when the signs multiply to positive, but if one of the signs is negative and the other positive, it gives the wrong lower bound.
The problem is that the plus-or-minus bd "depends" on the signs of b and d.
Is there a concise and succinct way to write this expression?