Expand Using the Binomial Theorem (3x+2)^2

Problem

(3*x+2)2

Solution

1. Identify the terms and the exponent for the binomial expansion (a+b)n where a=3*x b=2 and n=2

2. Apply the formula for the Binomial Theorem, 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)(3*x)2*(2)0+(2/1)(3*x)1*(2)1+(2/2)(3*x)0*(2)2)))

4. Evaluate the combinations and the powers of each term.

1*(9*x2)*(1)+2*(3*x)*(2)+1*(1)*(4)

5. Simplify the expression by multiplying the coefficients.

9*x2+12*x+4

Final Answer

(3*x+2)2=9*x2+12*x+4

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