Expand Using the Binomial Theorem (x-12)^2

Problem

(x−12)^2

Solution

1. Identify the terms of the binomial (a+b)^n where a=x b=−12 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

(x−12)^2=(2/0)x^2*(−12)^0+(2/1)x^1*(−12)^1+(2/2)x^0*(−12)^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 by performing the multiplication and exponentiation.

(1)*(x^2)*(1)+(2)*(x)*(−12)+(1)*(1)*(144)

6. Combine the simplified terms to find the final polynomial.

x^2−24*x+144

Final Answer

(x−12)^2=x^2−24*x+144

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