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)*b^k) 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)*y^0+(2/1)x^(2−1)*y^1+(2/2)x^(2−2)*y^2)))

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⋅x^2⋅1+2⋅x^1⋅y^1+1⋅1⋅y^2

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

x^2+2*x*y+y^2

Final Answer

(x+y)^2=x^2+2*x*y+y^2

Want more problems? Check here!