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The distributive property states a(b+c+d) = ab + ac + ad.

\(\frac{1}{2} (10x+20y+10z)=\frac{1}{2}(10x) + \frac{1}{2}(20y) + \frac{1}{2}(10z)\\\\=\boxed{\bf{5x+10y+5z}}\)

Distributive property must be applied to simplify. 

1/2 10x = 5x
1/2 20y = 10y
1/2 * 10z = 5z

Answer:  5x + 10y + 5z 

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