How do you use the binomial theorem to expand (2x+3y)^3

Question

How do you use the binomial theorem to expand this?

Answer 1

( 2x + 3y )^3

Solution :

( 2x + 3y )^2 = 4x^2 + 12xy + 9y^2

So,

( 4x^2 + 12xy + 9y^2 ) ( 2x + 3y ) = 8x^3 + 12x^2y + 24x^2y + 36xy^2 + 18xy^2 + 27y^3

=  8x^3 + 36x^2y + 54xy^2 + 27y^3

Thus, answer is 8x^3 + 36x^2y + 54xy^2 + 27y^3 .