Using Pascal's Triangle to simplify the expansion:
{:
(ul("exponent")," | pattern:",,,,,,),
(0,,1,,,,,),
(1,,1,1,,,,),
(2,,1,2,1,,,),
(color(lime)3,,color(magenta)1,color(magenta)3,color(magenta)3,color(magenta)1,,),
(4,,1,4,6,4,1,),
(5,,1,5,10,10,5,1),
(...,,...,,,,,)
:}
(2x+3y)^color(lime)3
color(white)("XXX")=color(magenta)1 * (2x)^3 * (3y)^0+color(magenta)3 * (2x)^2 * (3y)^1 + color(magenta)3 * (2x)^1 * (3y)^2 + color(magenta)1 * (2x)^0 * (3y)^3
color(white)("XXX")=color(white)("XXXXXXX")8x^3 +color(white)("XXXXX")36x^2y +color(white)("XXXXX") 54xy^2+color(white)("XXXXX")27y^3