Answer
$x^5+15x^4+90x^3+270x^2+405x+243$
Work Step by Step
We are given the expression:
$(x+3)^5$
Use the Binomial Theorem to expand the expression:
$(x+3)^5=\sum_{k=0}^5 \binom{5}{k}x^{5-k}3^k$
$=\binom{5}{0}x^53^0+\binom{5}{1}x^43^1+\binom{5}{2}x^33^2+\binom{5}{3}x^23^3+\binom{5}{4}x^13^4+\binom{5}{5}x^03^5$
$=x^5+5(3)x^4+10(9)x^3+10(27)x^2+5(81)x+243$
$=x^5+15x^4+90x^3+270x^2+405x+243$
