simplifying equations by factorization and grouping

Apr 2016
7
0
uk
hi everyone

i have a few questions on an assignment, due to rushed notes which i am struggling to make head nor tail of, i am struggling to understand the method to complete them.

6t^7x^9 - 8x^4t^9 = 0

i know these are not too hard as a lot of students in class finished the assignment very quickly, unfortunatly i am still scratching my head. can anyone explain a method to simplify the above equation so that i can put it into action?

thanks
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
6t^7x^9- 8x^4t^9

The first thing I would notice is that both "6" and "8" are even so I can factor out a "2": 2(3t^7x^9- 4x^4t^9). Further, x^9= x^4(x^5) so I can factor out "x^4": 2x^4(3t^7x^5- 4t^9). And t^9= t^7(t^2) so I can factor out "t^7": 3x^4t^7(3x^5- 4t^2). I do not believe that factors further (with integer coefficients and integer powers).
 
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Apr 2016
7
0
uk
Thank you for the help! (Happy)

I also have this problem, this is how i have tried to simplify it.


6y^2t^6 - 2y^2 - 9y^2t^6 = 0

I have:

6y^2t^6 = 2*3 y*y*t*t*t*t*t*t

2y^2 = 1*2 y*y

9y^2t^6 = 3*3 y*y*t*t*t*t*t*t

Surely the only number common to all in the first part is 1? :? 1*6, 1*2, and 1*9

then we have y^2 and t^6

so..

1y^2t^6 (this must now be taken out of each term)

(6yt)

so..

1y^2t^6(6yt)

What do you think? im not convinced i have everything correct
 

skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
Uhh ... No.

6y^2t^6 - 2y^2 - 9y^2t^6 = 0
Note the first and last terms are like terms, and can be combined ...

$-2y^2-3y^2t^6=0$

Common factor for the two terms is $-y^2$ ...

$-y^2(2 +3t^6)=0$

Only solution to the equation is $y=0$
 
Apr 2016
7
0
uk
I am struggling so much with understanding this. maths is a subject i have always struggled with. You must think im really slow.

do you know of any good links to help me to understand this a bit better? I could fluke these questions but i need to understand what i am doing as i will be doing this a lot more in the future. something with questions and then the answer below and how it was worked out would be ideal. im looking at how you have answered the question and cant figure out why you have put things where you have.

I have three questions on this and was hoping with the first one answered i could use that method to answer the rest, unfortunatley i am still confused....

thanks
 
Feb 2015
2,255
510
Ottawa Ontario
Hey Mark...fancy meeting you here :)