Expand Using the Binomial Theorem (a+b)^2

Problem

(a+b)2

Solution

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

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

(2/0)a(2−0)*b0+(2/1)a(2−1)*b1+(2/2)a(2−2)*b2)))

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⋅a2⋅1+2⋅a1⋅b1+1⋅1⋅b2

5. Simplify the expression to its final form.

a2+2*a*b+b2

Final Answer

(a+b)2=a2+2*a*b+b2

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