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I need help ASAP!!!

 

Assuming that  \(y\neq 1/2, \)simplify the expression \(\dfrac{12y^3-6y^2}{2y-1}. \)

 Aug 6, 2020
 #1
avatar+1038 
+5

Before you look at answer: Try to divide using long division... watch this video for more information: https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-long-division-of-polynomials/v/dividing-polynomials-1

 

Tried it already? Now, here is how I did it:

 What can you do to 12y^3-6y^2 to make it easier to divide? (*cough* factoring out a 6? *cough*) 

So, after I factored out a 6, I got 6*(2y^3-y^2)/(2y-1). This was easy to divide, and I got 6*y^2, which is 6y^2

 

OR

If you were smart enough to see if right after factoring, you could multiply the bottom by 6. This is 12y-6. Now, the difference between the top and the bottom? y^2. So, you still end up with 6y^2

 

:)

 Aug 6, 2020
edited by ilorty  Aug 6, 2020
 #2
avatar+21957 
+2

Hint:     12y3 - 6y2  =  6y2(2y - 1)

 Aug 6, 2020

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