Use the Binomial Theorem to expand the expression $(x+3y{)}^4$ .

A) $x^4+12x^{3}y+54x^2{y}^2+108x{y}^3+81y^4$
B) $x^4+3x^{3}y+9x^2{y}^2+27x{y}^3+81y^4$
C) $x^4+4x^{3}y+6x^2{y}^2+4x{y}^3+y^4$
D) $x^4+81y^4$
E) $x^4+15x^{3}y+90x^2{y}^2+135x{y}^3+81y^4$