I'm pretty sure this isn't a homework style question.(adsbygoogle = window.adsbygoogle || []).push({});

could someone please explain this, I may be overly tired, but it's confusing me:

"A further illustration of this rule is generally given by algebraists as follows: First, we know that +a multiplied by +b gives the product +ab; and if +a be multiplied by a quantity less than b, as in b-c, the product must necessarily be less than ab; in short, from ab we must subtract the product of a, multiplied by c; hence a times (b-c) must be expressed by ab-ac; therefore it follows that a times -c gives the product -ac. If now we consider the product arising from the multiplication of the two quantities (a-b), and (c-d), we know that it is less than that of (a-b) times c, or of ac-bc; in short, from this product we must subtract that of (a-b) times d; but the product (a-b) times (c-d) becomes ac-bc-ad, together with the product of -b times -d annexed; and the question is only what sign we must employ for this purpose, whether + or -. Now we have seen from that the product ac-bc we must subtract a quantity less than ad, we have therefore subtracted already too much by the quantity bd; this product must therefore be added; that is, it must have the + sign prefixed, hence we see that -b times -d gives +bd for a product; or -minus multiplied by -minus gives +plus."

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Algebraic explanation of - times - = +

**Physics Forums | Science Articles, Homework Help, Discussion**