A math problem of which I know the answer.?

Question

I come from Astronomy and Space. I saw this problem in a magazine and believe I got the right answer. I'd like to know if any of you could confirm. I will not give you my answer, though, in order not to facilitate your finding the solution. Here goes  :  If x and y are positive integers, which of the following is equivalent to (2x)^3y - (2x)^y.

  A. (2x)^2y

  B. 2^y(x^3 - x^y)

  C.  (2x)^y( (2x)^2y - 1  )

  D.  (2x)^y(4x^y - 1)
 
  E.  (2x)^y(  (2x)^3  -1  )

Hector Israel · Accepted Answer

C. Because you just need to factorize (2x)^3y - (2x)^y.

Anthony · Answer

C
(2x)^3y - (2x)^y = (2x)^y(2x^2y - 1)

PS
(2x)^3y = (2x)^y*(2x)^2y
(2x)^3y - (2x)^y =  (2x)^y*(2x)^2y - (2x)^y = (2x)^y[(2x)^2y - 1]

A math problem of which I know the answer.?

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