${{(3+x)}^{8}}={{[3(1+\tfrac{x}{3})]}^{8}}={{3}^{8}}{{(1+\tfrac{x}{3})}^{8}}$

${{(3+x)}^{8}}={{3}^{8}}\left[ 1{{+}^{8}}{{C}_{1}}(\tfrac{x}{3}){{+}^{8}}{{C}_{2}}{{(\tfrac{x}{3})}^{2}}{{+}^{8}}{{C}_{3}}{{(\tfrac{x}{3})}^{3}}{{+}^{8}}{{C}_{4}}{{(\tfrac{x}{4})}^{4}}{{+}^{8}}{{C}_{5}}{{(\tfrac{x}{3})}^{5}}{{+}^{8}}{{C}_{6}}{{(\tfrac{x}{3})}^{6}}{{+}^{8}}{{C}_{7}}{{(\tfrac{x}{3})}^{7}}+{{(\tfrac{x}{3})}^{8}} \right]$

${{(3+x)}^{8}}={{3}^{8}}\left[ 1+\tfrac{8x}{3}+\tfrac{28{{x}^{2}}}{{{3}^{2}}}+\tfrac{56{{x}^{3}}}{{{3}^{3}}}+\tfrac{70{{x}^{4}}}{{{3}^{4}}}+\tfrac{56{{x}^{5}}}{{{3}^{5}}}+\tfrac{28{{x}^{6}}}{{{3}^{6}}}+\tfrac{8{{x}^{7}}}{{{3}^{7}}}+\tfrac{{{x}^{8}}}{{{3}^{8}}} \right]$

${{(3+x)}^{8}}={{3}^{8}}+{{3}^{7}}\cdot 8x+{{3}^{6}}\cdot 28{{x}^{2}}+{{3}^{5}}\cdot 56{{x}^{3}}+{{3}^{4}}\cdot 70{{x}^{4}}+{{3}^{3}}\cdot 56{{x}^{4}}+{{3}^{2}}\cdot 28{{x}^{6}}+3\cdot 8{{x}^{7}}+{{x}^{8}}$

${{(3+x)}^{8}}=6561+17496x+20412{{x}^{2}}+113608{{x}^{3}}+5670{{x}^{4}}+1512{{x}^{5}}+252{{x}^{6}}+24{{x}^{7}}+{{x}^{8}}$