Expand Using the Binomial Theorem (x+y)^8

Problem

(x+y)8

Solution

1. Identify the parameters of the binomial expansion (a+b)n where a=x b=y and n=8

2. Apply the Binomial Theorem formula, which states that (a+b)n=(∑_k=0^n)((n/k))*a(n−k)*bk)

3. Determine the coefficients using the combination formula (n/k)=(n!)/(k!(n−k)!)) for k=0 through 8

4. Calculate the terms by multiplying each coefficient by the corresponding powers of x and y

5. Combine the terms into a single polynomial expression.

Final Answer

(x+y)8=x8+8*x7*y+28*x6*y2+56*x5*y3+70*x4*y4+56*x3*y5+28*x2*y6+8*x*y7+y8

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