# Multiplication explanation needed

• Jul 6th 2009, 02:12 PM
Sooda
Multiplication explanation needed
(b - c)(c - a)(a - b) = abc -a^2b - b^2c + ab^2 - ac^2 + a^2c + bc^2 - abc

Took it from thread http://www.mathhelpforum.com/math-he...z-help-me.html I have forgotten how multiplication worked with so many erm... numbers. He has reordered multiplications to look nicer, but it makes it hard to track where he started and ended it.

Can someone link me to tutorial which teaches such multiplication, has it a name? I am in this forum new and trying to learn expression simplifying. I will check tomorrow for replies.

By the way how he got so nice layout of that expression. I mean it is image stored on site, can I do same and learn how to "write" such images?
• Jul 6th 2009, 02:34 PM
Plato
There is no mystery to it.
Consider $\left( {a + b} \right)\left( {c + d} \right) = ac + ad + bc + bd$.
Look at the pattern. Start with a times c+d. Then go to b.
Do you see?

Now consider: $\left( {a + b} \right)\left( {c + d} \right)\left( {e + f} \right) = ace + acf + ade + adf + bce + bcf + bde + bdf$
Look at the pattern. Do you see?

Now apply it to your question.
$\left( {b - c} \right)\left( {c - a} \right)\left( {a - b} \right) = bca - bcb - baa - bab - cca + ccb + caa - cab$.
Do you see how it works.
• Jul 6th 2009, 07:13 PM
Stroodle
Here's a short tutorial:

YouTube - Trick 2 : Fast Algebra Multiplication -- Binomials

and here's a link for $LaTex$:

http://www.mathhelpforum.com/math-he...-tutorial.html
• Jul 7th 2009, 11:46 AM
Sooda
Thank you both. Plato that was exactly what I needed. Such simple examples help me learn.
Stroodle, nice now I can use LaTex instead of MS Paint. Just checked Youtube video and I have not seen something so awsome long time. Crusial things which I have to learn with step by step explanations. Going to find more similar videos. I am trying to relearn (reremember) simplifying expressions from school time.