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

Problem

(x+12)^2

Solution

1. Identify the terms and the exponent for the binomial expansion (a+b)^n where a=x b=12 and n=2

2. Apply the formula for the Binomial Theorem, which states (a+b)^n=(∑_k=0^n)((n/k))*a^(n−k)*b^k)

3. Write out the terms of the expansion using the combinations (2/0)) (2/1)) and (2/2))

(x+12)^2=(2/0)x^2*(12)^0+(2/1)x^1*(12)^1+(2/2)x^0*(12)^2)))

4. Calculate the binomial coefficients and the powers of 12.

(x+12)^2=1⋅x^2⋅1+2⋅x⋅12+1⋅1⋅144

5. Simplify each term to find the final polynomial.

(x+12)^2=x^2+24*x+144

Final Answer

(x+12)^2=x^2+24*x+144

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