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)*b^k)

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=x^8+8*x^7*y+28*x^6*y^2+56*x^5*y^3+70*x^4*y^4+56*x^3*y^5+28*x^2*y^6+8*x*y^7+y^8

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