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saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
Party time! :D
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
lol I dunno...
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
What can you teach me?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
a lot, there's a fair amount to algebra, but what's the next logical step?
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Teach about polynomial.
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
I have already to an extent, but where to go next...
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
In maths the fundamentals concepts are limited but the problems are not, so how about practicing what you have already learned?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
That's a good point FFM so lets do simplification that you know, but a little more intense: I think I need to make sure you can simplify bigger things:\[\frac{x^2y^5z}{xy^9z^3}\]
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
awww, you're making me think of my cat in the hospital :(
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
How did it go with her?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
broken leg... waiting for an operation
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
You beat you cat Turing?!!!
 2 years ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
turing sat on her leg. :(
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
she fell off the roof. how pessimistic
 2 years ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
awww, sorry i was jking..
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
It's all good :P
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Due to Turing's intense physics stress his cat decided to commit suicide :P
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
(x^2)*(y^5)*(z)  = (x)*(y^5/9)*(z^1/3)? (x)*(y^9)*(z^3)
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
why \( y^{5/9} \) ?
 2 years ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
no doubt. ;)
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
you have inconsistent rules above inopeki\[\frac{x^a}{x^b}=x^{ab}\]always...
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
(x^2)*(y^5)*(z)  = (x)*(y^59)*(z^13)? (x)*(y^9)*(z^3)
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
yes, simplify...
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
(x)*(y^59)*(z^13)=(x)*(y^4)*(z^2)?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
yes, do you know another way to write\[x^{a}\]???
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
\[x^{a}=\frac{1}{x^a}\]so it's probably nicer to rewrite your expression with all positive exponents in this way.
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
Oh right, all negative exponents make the "total number" divided by one.
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Btw who can explain why x^0 = 1?
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
(x)*(1/y^4)*(1/z^2)
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
Oh dear... I have my answers about x^0=1 (not true for x=0), but I'm sure FFM would not approve of them :/ @inopeki, yes now rewrite it as 1 fraction...
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Turing that's a very important yet fundamental question.
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
another one is why \( (a^b)^c = a^{bc} \) ?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
well I have a very simple proof of it and I can show why it is not true for x=0 what more do I need in your opinion?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
the last rule is easier to explain, perhaps I should...
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
(x)*(1/y^4)*(1/z^2) (x)*(1/y^4*z^2)?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
yes, now write it as a fraction what goes on the bottom? what goes on the top?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
@FFMactually that's not so easy to explain now that I think about it.
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Can you explain the second rule intuitively?
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
1 x*  y^4*z^2
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
no, I was thinking more of how easy it is to show x^ax^b=x^(a+b) intuitively, the other is tricky to me.
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
@ inopeki you can put the x on top, it means the same thing and looks nicer
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
x*1  y^4*z^2
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Can we say that all power function obeys the functional equation \( f(x)f(y)= f(x+y) \)?
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
Whats that f?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
@Inopeki yes, no need to write the 1 though @FFM, I'd have to think about that :/
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
unspecified functions he's asking how far the rule about exponents can be extended..
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
x  Oh right y^4*z^2
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Actually we can't but I believe that is true for exponential functions though.
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
it must be for simple ones\[2^x2^y=2^{x+y}\]of course
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Tha's whats Inopeki is using right ?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
basically Inopeki do you see the connection between what you are doing and the rule for multiplying exponents like\[x^ax^b\]?
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
Yeah, but does that mean that it becomes x  ? yz^6
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
no because y and z are different bases notice the rule above had both base x.
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
YEah but then i dont see the connection..
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
just that dividing and multiplying are inverse operations x^a=x*x*x*...*x (a times) x^b=x*x*x*...*x (b times) so if we have a=3 b=2 we get x^a  x^b x*x*x == x x*x which is x^(ab) if we have (x^a)(x^b) we get (x*x*x)(x*x)=x*x*x*x*x=x^(a+b) so the rules for exponents here come directly from their definitions. You can count the x and see that this relationship holds.
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
I know about that, like x^2*x^8=x^10
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
x^10/x^5=x^5
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
right, I want you to see how that and the rule for division are inverses of each other for a reason...
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Turing you have a heck of patience :D
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
eh it's easy FFM, doesn't require too much concentration. good practice too I learn by teaching ;) ok factor \[3x^3y^3+6xy+9x^2y\]
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
The GCF of 3,6,9 is 3 The GCF of x,x^2,x^3 is x The GCF of y,y^2,y^3 is y 3xy(3x^3*y^3/3xy)+3xy(6xy/3xy)+3xy(9x^2*y/3xy) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Middle step, right?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
yes exactly
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
3xy(3x^3*y^3/3xy)+3xy(6xy/3xy)+3xy(9x^2*y/3xy)=3xy(x^2*y^2+2+3x)?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
yep :) great!
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Note to Inopeki: Turing is a great resource, learn new things from him and practice as much as you can on your own :)
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
Yes I've stressed the importance of studying on your own as well and yes Inopeki really, FFM would have noticed a mistake I'm sure ok quick, foil (ab)(a+b)
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
When hes not here i try to go on purplemath and khan :)
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
a^2+abbab^2
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
simplify
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Books books books!! online learning has it's own limitation :)
 2 years ago

Akshay_Budhkar Group TitleBest ResponseYou've already chosen the best response.0
it doesnt @ffm i disagree
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
Foolformath, im having trouble finding books here in sweden
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
and what is the name of that form? remember?
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
The fundamental theorem of algebra? Or want that the one with the multiplex?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
Multiplex? no I think you're thinking of 'multiplicity' but this is the 'difference of squares' \[a^2b^2=(ab)(a+b)\]
 2 years ago

Akshay_Budhkar Group TitleBest ResponseYou've already chosen the best response.0
with ocw.mit , khan, purple math and openstudy and people like turing there is no limit to online education ^
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
Thanks but you get what you put in, I think is true with all this stuff.
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
The fundamental theorem of algebra: "the sum of the multiplicity of the roots of a polynomial is equal to its order" difference of squares\[a^2b^2=(ab)(a+b)\]both important, but very different
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
so remember that we can run this backwards, and I can say 'factor'\[x^24\]using difference of squares wanna try?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
run the FOIL backwards I meant*
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
no look at the form\[a^2b^2=(ab)(a+b)\]so what is a and b in\[x^24\]???
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
(x2)(x+2)?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
there ya go :)
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
how about\[x^4y^4\](this is a favorite question on OS)
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
(x^2y^2)(x^2+y^2)
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
good, now is that all we can do with it though? (I've seen a lot of tutors stop here too ;)
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
hint:look at the first set of parentheses
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
what is the first sett of parentheses?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
yes, and can you factor that?
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
GCF of x^2 is x GCF of y^2 is y xy(x^2/xy)xy(y^2/xy)?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
no you're overthinking x^2y^2 is difference of squares again!
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
\[a^2b^2=(ab)(a+b)\]
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
So (xy)(x+y)?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
yes! so now factor\[p^4q^4\]completely!!
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
you will apply difference of squares twice
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
(p^2q^2)(p^2+q^2) (pq)(p+q)(p+q)+(p+q)?
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
Without the +
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
between the parenthesis
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
(p^2q^2)(p^2+q^2) stop here we cannot factor the second set of parentheses, it is not a /difference/ of squares, it is a /sum/ of squares, and we have no formula for that. check that (a+b)(a+b) is not a^2+b^2 so only factor the one that is a /difference/ of squares
 2 years ago

Inopeki Group TitleBest ResponseYou've already chosen the best response.0
(pq)(p+q)(p^2+q^2) You said i had to do difference in squares 2 times? Btw, lets move to a new thread, this one is starting to lag a little bit
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.5
That is above correct, you did difference of squares twice: p^4q^4 (p^2q^2)(p^2+q^2) <once (pq)(p+q)(p^2+q^2) <twice ok new thread...
 2 years ago
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