Question

The coefficient of the third term in the expansion of the binomial (3x2 + 2y3)4 is_________

Answer 1

A binomial expansion is given by (a + b)^n = ∑nCk * a^(n - k) * b^k, k = 0, 1, 2 , . . . n
The third term is the term for k = 2.
The third term = 4C2 * (3x^2)^(4 - 2) * (2y^3)^2 = 6 * 9x^4 * 4y^6 = 216x^4y^6

Therefore, the coefficient of the third term is 216.

Answer 2

Use the binomial theorem.
2C4=4!/2!(4-2)!=24/4=6
3^2*2^2=9*4=36
36*6=216
216