SOLUTION: write the binomial expansion of (x+y) exponent 4 as a polynomial in simplest form.

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Question 668505: write the binomial expansion of (x+y) exponent 4 as a polynomial in simplest form.
Found 2 solutions by swincher4391, jim_thompson5910:
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
(x+y)^4 = (4 choose 0)x^4*y^0 + (4 choose 1)x^3*y^1 + (4 choose 2) x^2y^2 + (4 choose 3) x^1*y^3 + (4 choose 4) x^0*y^4 = x%5E4+%2B+4x%5E3y+%2B+6x%5E2y%5E2+%2B+4xy%5E3+%2B+y%5E4

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Look at row 5 in Pascals triangle to see these values: 1, 4, 6, 4, 1

These are the coefficients of each term in the form (x)^k*(y)^(n-k) where k starts at 4 and steps down to 0 (n and k are integers where n = 4)

So the expansion of (x+y)^4 is


1*(x)^4*(y)^0 + 4*(x)^3*(y)^1 + 6*(x)^2*(y)^2 + 4*(x)^1*(y)^3 + 1*(x)^0*(y)^4

1*(x^4)*(1) + 4*(x^3)*(y^1) + 6*(x^2)*(y^2) + 4*(x^1)*(y^3) + 1*(1)*(y^4)

x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4

Therefore the answer is: (x+y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4