Expand Using the Binomial Theorem (x+11)^2

Problem

(x+11)2

Solution

1. Identify the terms and the exponent for the binomial expansion (a+b)n where a=x b=11 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 for k=0 k=1 and k=2

(2/0)x2*11+(2/1)x1*11+(2/2)x0*11)))

4. Calculate the coefficients using the combination formula (n/k)=(n!)/(k!(n−k)!))

(2/0)=1)

(2/1)=2)

(2/2)=1)

5. Substitute and simplify each term:

1⋅x2⋅1+2⋅x⋅11+1⋅1⋅121

x2+22*x+121

Final Answer

(x+11)2=x2+22*x+121

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