Use the Banh nominal theorem to determine the expanded form of the by nominal expression

Apply the given theorem to find the expanded form of the given binomial, in this case n is 4:
[tex]\begin{gathered} =x^4+\frac{4}{1}x^{4-1}y+\frac{4(4-1)}{2}x^{4-2}y^2+\frac{4(4-1)(4-2)}{6}x^{4-3}y^3+y^4 \\ =x^4+4x^3y+6x^2y^2+4xy^3+y^4 \end{gathered}[/tex]The correct answer is this:
[tex]x^4+4x^3y+6x^2y^2+4xy^3+y^4^{}^{}^{}[/tex]