Where did RK go?

[alice]

ok, you just take out the (u-3) and multiply it by what's left (u+9), if that makes more sense.

[Tone]

THANK YOU ALICE!!

That does make sense! I was having so much trouble with that... now I can finish my homework, thanks so much!

[Rosebud]

Here Tone, does this help:

[url]http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut7_factor.htm[/url]

[Rosebud]

Oops, too late! Sorry, I was going to type it all out and then decided to find an easuer way and Alice beat me to it... oh well, Good Job Alice!

[Tone]

Hey that's pretty handy, RoseB - I understand most of it (thanks to our substitue teacher last Wednesday) but I'll have to remember to come back to that if I'm having trouble and neither alice, RK, nor bluesummer are online to hold my hand :]

[Rosebud]

For the most part, I know all that stuff but I forget somethings since I don't deal with every day and haven't for many years! But I'll help when I can!

[RSK]

Not to hijack... but while I have RK's attention, can you give me a hand?

Explain to me how

u(u-3) + 9(u-3)

factored completely = (u-3) (u+9)

?

Absolutely!

what you have, is TWO separate terms...

u(u-3) + 9(u-3)


frist, you want to factor out each term....

the FRIST term, u(u-3)

this translates to (u times u) minus (3 times u).....

.....it gives: u sqared minus 3u (for sake of clarity, * is a squared symbol)


so, we have u*-3u

the SECOND term, 9(u-3)

this translates to (9 times u) minus (9 times 3)....

......this gives: 9u - 27


okay, now lets comine BOTH terms together....


u* - 3u + 9u - 27



(I put the + sign in BOLD, so that you can see where it relates to from the question)...



this is a two step problem. you have allready done the FRIST step by factoring out...

now, you want to add common terms...


i'm gonna side track for a bit:

_________________________________________________
side notes:

when you have u + 2u, this equals 3u...

when you have 3x* + 2x*, this equals 5x*

when you have 3x* + x, this can't be done!!!!!!!!!!!


you might allready know this, but when i started algebra, i just couldn't comprehend WHY, and HOW, the above make sense...

..then a teacher taught me a NEW method, and it makes things SO MUCH more clear!!!!


think of the unknown terms (x, u, y, x*, or whatever), and think of them as APPLES and ORANGES!!!

this may sound crazy, but if you are having trouble with adding and subtracting terms, then this will DEFINATELY help!



for our sake, think of the u term as apples
think of the x* term, as oranges
and think of the x term, as pears...


now, back to the first three questions from above.....in stead of saying the letter, just say the FRUIT!!!

for the first one.....

1 apple + two apples = 3 apples (3u)

3 oranges + 2 oranges = 5 oranges (remember, orange is x*), so (5x*)

now, look at the next one...

we have 3 oranges + 1 pear ---> this cannot be 'simplified' further




well, what i just explained is VERY VERY basic, but when i first did algebra, the above method of thinking REALLY helped me a lot...
______________________________________________


back to the question..........

we have: u* - 3u + 9u - 27


so, combine 'like' terms, remember apples with apples, and oranges with oranges!


i see a +9u and a -3u, let's combine these!

to me, that translates to, 9 u's minus 3 of those u's, and that leaves us with 6 u's

so, we have

u* + 6u -27

ok, now this is probably the part where you actually need the help...

this is just trial and error. but it's NOT completely trial and error!!!



we must go from

u* + 6u -27

to

(u + 9)(u - 3)


here is how i do it:

let's do the FRIST term first: (u*), what must you multiply together, to get u* ?

well, u times u = u*

so, we have so far filled in the FRIST term of each bracket...

(u + ?)(u + ?)

now, lets to the LAST term...

what must you multiply together, to get -27?

well, there are MANY possibilities...

-1 and 27 (pos time neg = neg)
1 and -27
3 and -9
-3 and 9

so, we have four choices....

Okay,

....Next we have to determine the middle term, +6u .....

......of the pair of number above, which 'pair' 'add' to give +6?

that would be, the negative 3 and positive nine, (-3 and +9)

well, we can now fill in the question marks with these numbers




(u - 3)(u + 9)






the SAME reasoning can be applied to EVERY one of these types of questions, the numbers and terms may be different, but the overall outline of solving the problems is the SAME


math is all about practice...

...practice, practice, practice...



i LOVE math, because it's all about practice, and ONCE you solve a problem it feels GREAT!!! i use to SUCK at math! but i just opened book, and started doing problems.........

......sure i got a lot wrong, but with plenty of PRACTICE, i was able to learn from my mistakes...

...you are learning the FOUNDATIONS of math. You have a GREAT opportunity to learn what you are to the best of your ability. because when you get to higher levels, everything will 'build up'.

Trust me, do more problems............



........you will do great.......





if you have any other problems let me know, i'm more than willing to help








ok, i'm STARVING! i'm gonna get something to eat!

[RSK]

THANK YOU ALICE!!

That does make sense! I was having so much trouble with that... now I can finish my homework, thanks so much!

Oh.........GRRrrrreeeat! I just finish writing an essay on how to solve that two step problem, and now i get to read this post?

lucky me!



jk, i kid!



hey, good luck! in the post above, i put some VERY basic concepts. they helped ME! so i just wanted to share them, even if you allready now them.............

[alice]

glad i could help you. it makes me happy to get at least some kind of use out of all the sh*t i had to learn. i never understood why anybody would want to factor out u(u-3) + 9(u-3). the only thing you really need to know if you're going to study architecture is trigonometry.

[Rosebud]

RSK, you are such a great teacher!!!!

[misombra]

i can't WAIT till you take stats cause i will get you an A+ baby!

[Tone]

hahaha thanks RK!!

That did help me a lot - especially the apples/oranges/pears things! That DOES help it make a lot more sense!

And yeah, math does seem to be all about practice. Which is why I'm doing my homework now! We have assignments out of the book like everyday (like 100 problems, I'm not even joking) and we DON'T have to hand it in, it doesn't count for anything! Normally I'd be like SWEET - not doing it then!

But he says it's good idea to do it for PRACTICE and so to help understand what's going on so that we CAN do well on the quizes we DO have to take every single day.

Thanks again RK.. I will say that alice's way was much easier, just taking out u-3 leaves you with what? u + 9!

With a little more practice, and a little help from my internet friends - I think Lloyd is going to need to find something new to pick on me with - cause it won't be math for long!

Now I can relax a bit in class - I think today I'm going to switch seats to pick a seat next to this cute latina in my class. Thanks again!

[Tone]

i can't WAIT till you take stats cause i will get you an A+ baby!

Yeah??? That sounds great!

How you gonna do that? Gonna quiz me and play the game of "For each question you get right, I take off another article of clothing" ? Cause that's my favorite!

[alice]

Yeah??? That sounds great!

How you gonna do that? Gonna quiz me and play the game of "For each question you get right, I take off another article of clothing" ? Cause that's my favorite!

well, she won't need to wear more than her swimsuit, then, and there's still no chance of you seeing her naked!

[misombra]

no, you will have to behave yourself this time. we'll have to save that lesson for the special game of poker.