The value of 25³ – 75³ + 50³ + 3 × 25 × 75 × 50 is

The given expression can be rewritten as:

25³ – 75³ – (25 – 75)³ - 3(25)(75)(25 – 75)

As we know that,

(a – b)³ = a³ – b³ - 3ab(a - b)

⇒ a³ – b³ - (a – b)³ - 3ab(a - b) = 0

Since we can easily compare the above equation with the given expression by putting a = 25 and b = 75, the value of given expression is 0.