What is the third term in the binomial expansion of (3x+y^3)^4

The last choice is the one you want.

Step-by-step explanation:

Use the 5th row of Pascal's Triangle.  Since you have a 4th degree polynomial, there will be 5 terms in it.  The 5 coefficients, in order, are:

1, 4, 6, 4, 1

We will use these coefficients only up to and including the third one, since that is the one you want.  Binomial expansion using Pascal's Triangle looks like this:

That third term is the one we are interested in.  That simplification gives us:

Multiply 6 and 9 to get 54, and a final term of:

step-by-step explanation: