Expand Using the Binomial Theorem (3x+4)^2

Problem

(3*x+4)2

Solution

1. Identify the terms and the exponent for the binomial expansion (a+b)n where a=3*x b=4 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 expansion using the combinations (2/0)) (2/1)) and (2/2))

(2/0)(3*x)2*(4)0+(2/1)(3*x)1*(4)1+(2/2)(3*x)0*(4)2)))

4. Evaluate the combinations where (2/0)=1) (2/1)=2) and (2/2)=1)

1*(9*x2)*(1)+2*(3*x)*(4)+1*(1)*(16)

5. Simplify each term by performing the multiplication.

9*x2+24*x+16

Final Answer

(3*x+4)2=9*x2+24*x+16

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