Question

expand the expression:

\\((x + 3)^5 =\\)

Explanation:

Step1: Apply binomial theorem

$$(x + 3)^5 = \sum_{k=0}^{5} \binom{5}{k} x^{5-k} 3^k$$

Step2: Write out terms

$$\binom{5}{0}x^5(3)^0 + \binom{5}{1}x^4(3)^1 + \binom{5}{2}x^3(3)^2 + \binom{5}{3}x^2(3)^3 + \binom{5}{4}x^1(3)^4 + \binom{5}{5}x^0(3)^5$$

Step3: Calculate coefficients

$$1x^5(1) + 5x^4(3) + 10x^3(9) + 10x^2(27) + 5x(81) + 1(1)(243)$$

Step4: Simplify the expression

$$x^5 + 15x^4 + 90x^3 + 270x^2 + 405x + 243$$

Answer:

\(x^5 + 15x^4 + 90x^3 + 270x^2 + 405x + 243\)