Stuck on algebra, help please! (1 Viewer)

[wantingtoknow]

I think it's algebra...

anyway, is there an easier way to do this question rather than multiplying everything in and then simplifying it

expand and simplify (a+b+c)(a²+b²+c²-ab-bc-ca)

thank you!

 

[IamBread]

Not that I know of, I'm afraid you'll have to do it the long way.

 

[such_such]

I think it's algebra...

anyway, is there an easier way to do this question rather than multiplying everything in and then simplifying it

expand and simplify (a+b+c)(a²+b²+c²-ab-bc-ca)

thank you!

Looking at the structure, you can tell it's the sum of 3 cubes. And to simply it, all you need to do is cube everything separately in the first bracket. Then you minus the next step. Multiply how much terms there are in the first bracket (in this case 3) by the multiple of all the terms in the first bracket, (abc), therefore the second part will be -3abc

answer: <a href="http://www.codecogs.com/eqnedit.php?latex=a^{3}@plus;b^{3}@plus;c^{3}@plus;3abc" target="_blank"><img src="http://latex.codecogs.com/gif.latex?a^{3}+b^{3}+c^{3}-3abc" title="a^{3}+b^{3}+c^{3}+3abc" /></a>

You could do this for 4,5.....10 terms. One of those rules most school don't teach you.

Sorry it's a bit unclear, just procrastinating.

 

[wantingtoknow]

oh hmm, thank you. under what circumstances will this thing work?
how do you know when you can apply this rule and when you cannot?

 

[zeebobDD]

oh hmm, thank you. under what circumstances will this thing work?
how do you know when you can apply this rule and when you cannot?

you can apply it when terms are structured out like that, what you need to realise is that
when you multiply a by the b², it becomes ab², though when the b multiplies into the -ab it will become -ab², thus those two cancel out, and when you recognise the pattern it will be similar for all three of the first terms, but theres nothing common to cancel out with the a^3, b^3, etc... hence the answer such_such said

 

[wantingtoknow]

yeah, I can kind of see it lol. thanks

 

[zeebobDD]

yeah, I can kind of see it lol. thanks

was that a sarcastic comment?:L

 

[wantingtoknow]

no, I can actually see it lol. but I don't think I'll take that shortcut in exams hah