What is the 5th term of the expansion of (3x+y^4)^7

9514 1404 393

  945x^3·y^16

Step-by-step explanation:

The 5th term will be ...

  C(7,4)(3x)^3(y^4)^4 = 35·27·x^3·y^(4·4)

  = 945x^3·y^16

The coefficients of the expansion are C(n, k) where n is the exponent of the binomial, and k+1 is the term number. This is n!/(k!(n-k)!). The general (k-th) term of the expansion (a+b)^n is C(n, k)a^(n-k)b^(k) where k ranges from 0 to n.