# simplifying equations by factorization and grouping

#### mark78

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
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).

1 person

#### mark78

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
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 $y=0$

#### mark78

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

#### DenisB

Hey Mark...fancy meeting you here

#### mark78

Hey Mark...fancy meeting you here
The sosmaths forum? i did consider it was you earlier (Ottawa Ontario gave it away) (Smirk)

Mais oui.