What is expand (e^p)*(1+(3p^{1/2})/2) ?

The solution to expand (e^p)*(1+(3p^{1/2})/2) is e^p+(3e^pp^{1/2})/2

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expand (e^p)*(1+(3p^{1/2})/2)

expand

(e^{p}) \cdot (1 + \frac{3 p ^{\frac{1}{2}}}{2})

e^{p} + \frac{3 e ^{p} p ^{\frac{1}{2}}}{2}

Solution steps

(e^{p}) (1 + \frac{3 p ^{\frac{1}{2}}}{2})

Apply the distributive law:

a (b + c) = ab + a c

a = (e^{p}), b = 1, c = \frac{3 p ^{\frac{1}{2}}}{2}

= (e^{p}) \cdot 1 + (e^{p}) \frac{3 p ^{\frac{1}{2}}}{2}

= 1 \cdot (e^{p}) + \frac{3 p ^{\frac{1}{2}}}{2} (e^{p})

Simplify

1 \cdot (e^{p}) + \frac{3 p ^{\frac{1}{2}}}{2} (e^{p}) : e^{p} + \frac{3 e ^{p} p ^{\frac{1}{2}}}{2}

= e^{p} + \frac{3 e ^{p} p ^{\frac{1}{2}}}{2}

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\frac{2 x ^{2} + 10 x - 3}{( x + 1 ) ( x ^{2} - 9 )}

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What is expand (e^p)*(1+(3p^{1/2})/2) ?
The solution to expand (e^p)*(1+(3p^{1/2})/2) is e^p+(3e^pp^{1/2})/2