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

Problem

(x+2)2

Solution

1. Identify the terms and the exponent for the binomial expansion (a+b)n where a=x b=2 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 terms of the expansion using the combinations (2/0)) (2/1)) and (2/2))

(2/0)x2*2+(2/1)x1*2+(2/2)x0*2)))

4. Evaluate the combinations and powers.

1⋅x2⋅1+2⋅x⋅2+1⋅1⋅4

5. Simplify each term to find the final polynomial.

x2+4*x+4

Final Answer

(x+2)2=x2+4*x+4

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