Expand Using the Binomial Theorem (x+y)^6

Problem

(x+y)6

Solution

1. Identify the parameters of the binomial expression (a+b)n where a=x b=y and n=6

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

3. Determine the coefficients using the 6th row of Pascal's Triangle or the combination formula (6/k)) The coefficients for n=6 are 1, 6, 15, 20, 15, 6, 1$.

4. Write out the terms by decreasing the power of x from 6 to 0 and increasing the power of y from 0 to 6.

5. Combine the coefficients with the variables to form the final polynomial.

Final Answer

(x+y)6=x6+6*x5*y+15*x4*y2+20*x3*y3+15*x2*y4+6*x*y5+y6

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