1. ## Symplify

Hi!
I would like to know if there is any shortcut to the given statement:

(a-x)(b-x).......(z-x)

Solving it by opening all the parentheses is not, according to me, a very sensible thing to do here.
Any other rule which can be applied to simplify it?

Thanks a Lot!
~MoniMini

2. ## Re: Symplify

Originally Posted by MoniMini
Hi!
I would like to know if there is any shortcut to the given statement:
(a-x)(b-x).......(z-x)
Solving it by opening all the parentheses is not, according to me, a very sensible thing to do here.
Any other rule which can be applied to simplify it?

Would $\displaystyle (x-x)$ be one of the factors?

3. ## Re: Symplify

Ummm.....Well....how??
I'm not really understanding this.
I've already gone on Google and searched this, all the answers say is that (x -x) is the factor, but I don't really
understand how....

4. ## Re: Symplify

Originally Posted by MoniMini
Ummm.....Well....how??
I'm not really understanding this.
I've already gone on Google and searched this, all the answers say is that (x -x) is the factor, but I don't really understand how....

Look at the pattern:
$\displaystyle (a-x)$ times, $\displaystyle (b-x)$ times, $\displaystyle (c-x)$ times, until we get to $\displaystyle (z-x)$ times.

5. ## Re: Symplify

Okay, so what?
(I'm sorry if you're if you feel I'm annoying you but this is not from my school course, just a question which popped out from some higher-class book, and it really intrigues me)

Anyways, thanks

6. ## Re: Symplify

Originally Posted by MoniMini
Okay, so what?
(I'm sorry if you're if you feel I'm annoying you but this is not from my school course, just a question which popped out from some higher-class book, and it really intrigues me)

The answer is $\displaystyle 0$. That because $\displaystyle x-x=0$ so $\displaystyle 0$ times the rest is $\displaystyle 0$.

7. ## Re: Symplify

Uh-Oh....
I can understand that but I don't understand why the factor is (x-x).

8. ## Re: Symplify

Go through the alphabet. Surely you'll get to x if you go a, b, c, d, ...

Of course, this is assuming that you're using the symbol x from the alphabet to represent the same thing as the variable x in the statement, which it is quite likely you are not... But if that wasn't the case it would not be so easy to solve.

9. ## Re: Symplify

Aaaah! How silly I am!! Hehehe. I got it now :P