What is expand n^{1/2}(1+ln|n|) ?

The solution to expand n^{1/2}(1+ln|n|) is n^{1/2}+n^{1/2}ln|n|

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expand n^{1/2}(1+ln|n|)

expand

n^{\frac{1}{2}} (1 + ln ∣ n ∣)

n^{\frac{1}{2}} + n^{\frac{1}{2}} ln ∣ n ∣

Solution steps

n^{\frac{1}{2}} (1 + ln ∣ n ∣)

Apply the distributive law:

a (b + c) = ab + a c

a = n^{\frac{1}{2}}, b = 1, c = ln ∣ n ∣

= n^{\frac{1}{2}} \cdot 1 + n^{\frac{1}{2}} ln ∣ n ∣

= 1 \cdot n^{\frac{1}{2}} + n^{\frac{1}{2}} ln ∣ n ∣

Multiply:

1 \cdot n^{\frac{1}{2}} = n^{\frac{1}{2}}

= n^{\frac{1}{2}} + n^{\frac{1}{2}} ln ∣ n ∣

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What is expand n^{1/2}(1+ln|n|) ?
The solution to expand n^{1/2}(1+ln|n|) is n^{1/2}+n^{1/2}ln|n|