Expand Using the Binomial Theorem (x-6)^2

Problem

(x−6)^2

Solution

1. Identify the terms and the exponent for the binomial expansion (a+b)^n where a=x b=−6 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 the expansion by substituting the values into the formula for k=0,1,2

(2/0)(x)^2*(−6)^0+(2/1)(x)^1*(−6)^1+(2/2)(x)^0*(−6)^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⋅x^2⋅1+2⋅x⋅(−6)+1⋅1⋅36

x^2−12*x+36

Final Answer

(x−6)^2=x^2−12*x+36

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