What is expand e^θ(-θt+(t^2)/2) ?

The solution to expand e^θ(-θt+(t^2)/2) is -e^θθt+(e^θt^2)/2

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expand e^θ(-θt+(t^2)/2)

expand

e^{θ} (- θt + \frac{t ^{2}}{2})

- e^{θ} θt + \frac{e ^{θ} t ^{2}}{2}

Solution steps

e^{θ} (- θt + \frac{t ^{2}}{2})

Apply the distributive law:

a (b + c) = ab + a c

a = e^{θ}, b = - θt, c = \frac{t ^{2}}{2}

= e^{θ} (- θt) + e^{θ} \frac{t ^{2}}{2}

Apply minus-plus rules

+ (- a) = - a

= - e^{θ} θt + e^{θ} \frac{t ^{2}}{2}

Multiply

e^{θ} \frac{t ^{2}}{2} : \frac{e ^{θ} t ^{2}}{2}

= - e^{θ} θt + \frac{e ^{θ} t ^{2}}{2}

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What is expand e^θ(-θt+(t^2)/2) ?
The solution to expand e^θ(-θt+(t^2)/2) is -e^θθt+(e^θt^2)/2