Expand the binomial (3x^2 + 2y^3)^4. the coefficient of the third term in the expansion of the binomial (3x2 + 2y3)4 is

To expand a binomial of the form , we are going to use Pascal's triangle.
We can infer from our problem that , , and . Since , we are going to use the fourth row of Pascal's triangle to get the coefficients of our expansion, so the coefficients of our expansion will be: 1      4     6     4     1
Now that we have our coefficients, we cant expand our binomial:




Since the third term of the expansion is , we can conclude that the coefficient of the third term is 216.

The mode of the numbers is 29.