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

1 Answer

4 votes

9514 1404 393

Answer:

945x^3·y^16

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

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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.

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