Which of the options below is equivalent to 216x³ + 27y³ + 324x²y + 162xy²?

Correct option is A

Given Expression:

216x³ + 27y³ + 324x²y + 162xy² 

Identity  Used:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Solution:

Group the terms:

= 216x³ + 324x²y + 162xy² + 27y³

= 27(8x³ + 12x²y + 6xy² + y³)

Here, a = 2x, b = y

=> (2x + y)³ = 8x³ + 12x²y + 6xy² + y³

So, the simplified expression is:

= 27(2x + y)³ = (6x + 3y)³