Expand Using the Binomial Theorem (x+1)^2

Problem

(x+1)2

Solution

1. Identify the terms and the exponent for the binomial expansion (a+b)n where a=x b=1 and n=2

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

3. Write out the terms using the combinations (2/0)) (2/1)) and (2/2))

(x+1)2=(2/0)x2*(1)0+(2/1)x1*(1)1+(2/2)x0*(1)2)))

4. Calculate the coefficients where (2/0)=1) (2/1)=2) and (2/2)=1)

(x+1)2=1*(x2)*(1)+2*(x)*(1)+1*(1)*(1)

5. Simplify the expression by performing the multiplication.

(x+1)2=x2+2*x+1

Final Answer

(x+1)2=x2+2*x+1

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