Hi,

the sum of two  integers and is 4 times the smaller. 

Question states***

 x + y = 4x   Or 

Question also states***

the positive difference of their squares is 8 times the larger

 y^2 - x^2 = 8y

 (3x)^2 - x^2 = 8(3x)

  9x^2 - x^2 = 24x

  8x^2 - 24x = 0

 8x(x - 3) = 0

 8x = 0 ,  x = 0   Toss out this solution (0 is not a positive integer)

0r 

(x - 3) = 0 , x = 3  and  y = 9

and...  

Product of the two integers is 27

  

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