Question

expand the expression:

\\((3x + 1)^4 =\\)

Explanation:

Step1: Apply Binomial Theorem

$$(3x + 1)^4 = \sum_{k=0}^{4} \binom{4}{k} (3x)^{4-k} (1)^k$$

Step2: Write out terms

$$\binom{4}{0}(3x)^4 + \binom{4}{1}(3x)^3(1) + \binom{4}{2}(3x)^2(1)^2 + \binom{4}{3}(3x)(1)^3 + \binom{4}{4}(1)^4$$

Step3: Evaluate coefficients

$$1(81x^4) + 4(27x^3) + 6(9x^2) + 4(3x) + 1(1)$$

Step4: Simplify expression

$$81x^4 + 108x^3 + 54x^2 + 12x + 1$$

Answer:

\(81x^4 + 108x^3 + 54x^2 + 12x + 1\)