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)*b^k)

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

5. Simplify each term by multiplying the constants.

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

Final Answer

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

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