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)*b^k)

3. Write out the terms for k=0 k=1 and k=2

(2/0)x^2*11^0+(2/1)x^1*11^1+(2/2)x^0*11^2)))

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⋅x^2⋅1+2⋅x⋅11+1⋅1⋅121

x^2+22*x+121

Final Answer

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

Want more problems? Check here!