Expand Using the Binomial Theorem (2x+1)^2

Problem

(2*x+1)^2

Solution

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

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

4. Calculate the coefficients using the formula (n/k)=(n!)/(k!(n−k)!))

(2/0)=1)

(2/1)=2)

(2/2)=1)

5. Simplify each term by performing the exponentiation and multiplication:

1⋅4*x^2⋅1+2⋅2*x⋅1+1⋅1⋅1

4*x^2+4*x+1

Final Answer

(2*x+1)^2=4*x^2+4*x+1

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