Expand the following : ( 3a + 2b )3

The formula for ( a + b )³  is ( a + b )³ = a³ + 3a²b + 3ab² + b^3.

Now, in the given expression ( 3a + 2b ) ³, a = 3ab, b = 2b.

Expanding the expression using the above formula,

( 3a + 2b ) ³ = ( 3a ) ³ + 3( 3a) ² ( 2b) + 3( 3a)(2b) ² + ( 2b) ³

27a³  + ( 9a² )(6b) + ( 9a )( 4b² ) + 8b³

27a³ + 54a²b + 36ab² + 8b³

Hence, the correct option is B, i.e. 27a³ + 54a²b + 36ab² + 8b³.