Q. If a, b, c and d are four odd perfect cube numbers then which is always a factor of  

(∛a+∛b)^2 (∛c+∛d)

Ans : Let a = 1, b = 8, c = 125 and d = 343 are the four odd perfect cube numbers.

        Now ∛a=∛1=1,∛b=∛8=2,∛c=∛125=5  and ∛d=∛343=7                    

        (∛a+∛b)^2 (∛c  ∛d) be 192, 360, 512, 576 and 600.

        g.c.d (192, 360, 512, 576, 600) = 8

        ∴ 8 is always a factor of  (∛a+∛b)^2 (∛c+∛d) where a, b, c and d are four odd  

        perfect cube numbers.

Thank you for asking this question. Here is your answer:

a = 1

b = 8

c = 125

d = 343

These are the four odd perfect cube numbers.

∛a=∛1=1,∛b=∛8=2,∛c=∛125=5  and ∛d=∛343=7  

(∛a+∛b)^2 (∛c  ∛d) will be 192, 360, 512, 576 and 600

(192, 360, 512, 576, 600) = 8

So this means that 8 will always be the factor of (∛a+∛b)^2 (∛c+∛d)

If there is any confusion please leave a comment below.