Answer
$(2+ \frac{x}{2})^{5}=32+40x+20x^{2}+5x^{3}+\frac{5}{8}x^{4}+\frac{1}{32}x^{5}$
Work Step by Step
We use the values from the 5th row of Pascal's Triangle to find the coefficients:
$(2+ \frac{x}{2})^{5}=(2)^{5}+5(2)^{4}(\frac{x}{2})^1+10(2)^{3}(\frac{x}{2})^{2}+10(2)^{2}(\frac{x}{2})^{3}+5(2)^1(\frac{x}{2})^{4}+(\frac{x}{2})^{5}=32+40x+20x^{2}+5x^{3}+\frac{5}{8}x^{4}+\frac{1}{32}x^{5}$
