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 the expansion by substituting the values into the formula for k=0,1,2

(x−11)2=(2/0)x2*(−11)0+(2/1)x1*(−11)1+(2/2)x0*(−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. Simplify each term in the expression.

(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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