Answer:
12xy³
Step-by-step explanation:
The expansion of (3x+y)⁴ using the binomial theorem is:
[tex](3x + y)^4 = \binom{4}{0}(3x)^4y^0 + \binom{4}{1}(3x)^3y^1 + \binom{4}{2}(3x)^2y^2 + \binom{4}{3}(3x)^1y^3 + \binom{4}{4}(3x)^0y^4[/tex]
Simplifying:
[tex]\binom{4}{0}(3x)^4y^0 = 81x^4\\\\\binom{4}{1}(3x)^3y^1 = 108x^3y\\\\\binom{4}{2}(3x)^2y^2 = 36x^2y^2\\\\\binom{4}{3}(3x)^1y^3 = 12xy^3\\\\\binom{4}{4}(3x)^0y^4 = y^4\\\\[/tex]
So, the fourth term is 12xy³
