SOLUTION: Find the specified nth term in the expansion of the binomial. (Write the expansion in descending powers of x.) {{{ (4x+5y)^6 }}} , n=4

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Question 972748: Find the specified nth term in the expansion of the binomial. (Write the expansion in descending powers of x.)
, n=4
Found 2 solutions by Edwin McCravy, MathTherapy:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
, n=4






Edwin
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Find the specified nth term in the expansion of the binomial. (Write the expansion in descending powers of x.)
, n=4
Use the formula for a specific term of a binomial expansion:

(a + b)n = nC(r - 1) * (a)(n - (r - 1)) * (b)(r - 1)



We have: , with:





Term number, or 



  (a + b)n   = nC(r - 1) * (a)(n - (r - 1)) * (b)(r - 1)

4th term of: (4x + 5y)6:   6C(4 - 1) * (4x)(6 - (4 - 1)) * (5y)(4 - 1)

4th term of (4x + 5y)6:    6C3 * (4x)3 * (5y)3

4th term of (4x + 5y)6:    20 * 64x3 * 125y3

4th term of :    

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