Expand Using the Binomial Theorem (x+y)^2

Problem

(x+y)2

Solution

1. Identify the parameters for the Binomial Theorem formula (a+b)n=(∑_k=0^n)((n/k))*a(n−k)*bk) where a=x b=y and n=2

2. Write the summation terms for k=0 k=1 and k=2

(2/0)x(2−0)*y0+(2/1)x(2−1)*y1+(2/2)x(2−2)*y2)))

3. Calculate the binomial coefficients (n/k))

(2/0)=1)

(2/1)=2)

(2/2)=1)

4. Substitute the coefficients and simplify the exponents.

1⋅x2⋅1+2⋅x1⋅y1+1⋅1⋅y2

5. Combine the terms to reach the final expanded form.

x2+2*x*y+y2

Final Answer

(x+y)2=x2+2*x*y+y2

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