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

Problem

(4*x+3)2

Solution

1. Identify the terms of the binomial (a+b)n where a=4*x b=3 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 coefficients from the second row of Pascal's Triangle (1, 2, 1$).

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

4. Evaluate the combinations and powers.

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

5. Simplify each term by multiplying the constants.

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

Final Answer

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

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