What is expand (t-2)^3e^{3t} ?

The solution to expand (t-2)^3e^{3t} is e^{3t}t^3-6e^{3t}t^2+12e^{3t}t-8e^{3t}

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expand (t-2)^3e^{3t}

expand

(t - 2)^{3} e^{3 t}

e^{3 t} t^{3} - 6 e^{3 t} t^{2} + 12 e^{3 t} t - 8 e^{3 t}

Solution steps

(t - 2)^{3} e^{3 t}

(t - 2)^{3} = t^{3} - 6 t^{2} + 12 t - 8

= e^{3 t} (t^{3} - 6 t^{2} + 12 t - 8)

= e^{3 t} (t^{3} - 6 t^{2} + 12 t - 8)

Distribute parentheses

= e^{3 t} t^{3} + e^{3 t} (- 6 t^{2}) + e^{3 t} \cdot 12 t + e^{3 t} (- 8)

Apply minus-plus rules

+ (- a) = - a

= e^{3 t} t^{3} - 6 e^{3 t} t^{2} + 12 e^{3 t} t - 8 e^{3 t}

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

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

2 (x + y^{2}) d x + (y - x) d y

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

What is expand (t-2)^3e^{3t} ?
The solution to expand (t-2)^3e^{3t} is e^{3t}t^3-6e^{3t}t^2+12e^{3t}t-8e^{3t}