SOLUTION: Write and simplify only the specified term: The fourth term of (x + y)^7

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Question 920319: Write and simplify only the specified term:
The fourth term of (x + y)^7
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The fourth term of %28x+%2B+y%29%5E7
%28x+%2B+y%29%28x+%2B+y%29%28x+%2B+y%29%28x+%2B+y%29%28x+%2B+y%29%28x+%2B+y%29%28x+%2B+y%29
%28x%5E2%2B2xy%2By%5E2%29%28x%5E2%2B2xy%2By%5E2%29%28x%5E2%2B2xy%2By%5E2%29%28x+%2B+y%29
%28x%5E4%2B4x%5E3y%2B6x%5E2y%5E2%2B4xy%5E3%2By%5E4%29%28x%5E3%2B3x%5E2y%2B3xy%5E2%2By%5E3%29

The fourth term is highlight%2835x%5E4y%5E3%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Write and simplify only the specified term:
The fourth term of (x + y)^7


%28x+%2B+y%29%5E7 

Use the Binomial Expansion Formula: (a + b)n = nCr-1 * a [n -(r - 1)] * b r - 1  to determine the 4th term

With a = x;  b = y  ;  r, or term number = 4; and n = 7,

(a + b)n = nCr-1 * a [n -(r - 1)] * b r - 1  becomes:

(x + y)7 = 7C4-1 * x [7 -(4 - 1)] * y 4 - 1 

(x + y)7 = 7C3 * x 4 * y 3

(x + y)7 = 35x4y3