What is expand-1/4 (6e^{x/2}+e^x) ?

The solution to expand-1/4 (6e^{x/2}+e^x) is -3/2 e^{x/2}-1/4 e^x

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expand-1/4 (6e^{x/2}+e^x)

expand

- \frac{1}{4} (6 e^{\frac{x}{2}} + e^{x})

- \frac{3}{2} e^{\frac{x}{2}} - \frac{1}{4} e^{x}

Solution steps

- \frac{1}{4} (6 e^{\frac{x}{2}} + e^{x})

Apply the distributive law:

a (b + c) = ab + a c

a = - \frac{1}{4}, b = 6 e^{\frac{x}{2}}, c = e^{x}

= - \frac{1}{4} \cdot 6 e^{\frac{x}{2}} + (- \frac{1}{4}) e^{x}

Apply minus-plus rules

+ (- a) = - a

= - 6 \cdot \frac{1}{4} e^{\frac{x}{2}} - \frac{1}{4} e^{x}

6 \cdot \frac{1}{4} e^{\frac{x}{2}} = \frac{3}{2} e^{\frac{x}{2}}

= - \frac{3}{2} e^{\frac{x}{2}} - \frac{1}{4} e^{x}

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

(x - 4 - 6) (x - 4 + 6)

x^{2} + (y + 1)^{2}

e^{x} (x + 4)

(x - 3 - 5) (x - 3 + 5)

What is expand-1/4 (6e^{x/2}+e^x) ?
The solution to expand-1/4 (6e^{x/2}+e^x) is -3/2 e^{x/2}-1/4 e^x