SOLUTION: Hello. I need to find the greatest common divisor of: {{{3y^3-27y}}} and {{{6y^3)+12y^2-90y}}} I know to pull out 3y from the first expression to get: {{{3y(y^2-9)}}}

Algebra ->  Expressions-with-variables -> SOLUTION: Hello. I need to find the greatest common divisor of: {{{3y^3-27y}}} and {{{6y^3)+12y^2-90y}}} I know to pull out 3y from the first expression to get: {{{3y(y^2-9)}}}       Log On


   

Question 316254: Hello. I need to find the greatest common divisor of:
3y%5E3-27y and 6y%5E3%29%2B12y%5E2-90y
I know to pull out 3y from the first expression to get:
3y%28y%5E2-9%29
and 6y from the second expression to get:
6y%28y%5E2%2B2y-15%29
However, I do not know how to progress to the answer 3y%5E2-9y as the GCD. If you could help me, it would be much appreciated!
~hbanana

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Hello. I need to find the greatest common divisor of:
3y%5E3-27y and 6y%5E3%29%2B12y%5E2-90y
I know to pull out 3y from the first expression to get:
3y%28y%5E2-9%29.

Right there you need to factor the red%28%28y%5E2-9%29%29 as red%28%28y-3%29%28y%2B3%29%29
and get:

red%283y%28y-3%29%28y%2B3%29%29.

and 6y from the second expression to get:
6y%28y%5E2%2B2y-15%29 

Right there you need to factor the red%28%28y%5E2%2B2y-15%29%29 as red%28%28y-3%29%28y%2B5%29%29
and get:

red%286y%28y-3%29%28y%2B5%29%29

So you have to get the GCD of

red%283y%28y-3%29%28y%2B3%29%29 and red%286y%28y-3%29%28y%2B5%29%29

They have factors red%283%29, red%28y%29, and red%28%28y-3%29%29 in common.

So the GCF is 3y%28y-3%29 which when multiplied out gives 3y%5E2-9y

Edwin