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

The solution to expand-(t-3)^2e^{t-3} is -e^{t-3}t^2+6e^{t-3}t-9e^{t-3}

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

expand

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

- e^{t - 3} t^{2} + 6 e^{t - 3} t - 9 e^{t - 3}

Solution steps

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

(t - 3)^{2} = t^{2} - 6 t + 9

= - e^{t - 3} (t^{2} - 6 t + 9)

= - e^{t - 3} (t^{2} - 6 t + 9)

Distribute parentheses

= (- e^{t - 3}) t^{2} + (- e^{t - 3}) (- 6 t) + (- e^{t - 3}) \cdot 9

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= - e^{t - 3} t^{2} + 6 e^{t - 3} t - 9 e^{t - 3}

\frac{x + y}{( x - 1 ) ( x - 2 )}

sin^{3} (x) cos (x) (sin^{3} (x) + cos (2 x))

- \frac{1}{2} s (s + 1) (s + 5) (s + 10)

(1 + sin (a)) (1 - sin (a)) - cos^{2} (a)

What is expand-(t-3)^2e^{t-3} ?
The solution to expand-(t-3)^2e^{t-3} is -e^{t-3}t^2+6e^{t-3}t-9e^{t-3}