What is expand-48t^2e^{-t^2+2t}*(2t-2) ?

The solution to expand-48t^2e^{-t^2+2t}*(2t-2) is -96e^{-t^2+2t}t^3+96e^{-t^2+2t}t^2

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expand-48t^2e^{-t^2+2t}*(2t-2)

expand

- 48 t^{2} e^{- t^{2} + 2 t} \cdot (2 t - 2)

- 96 e^{- t^{2} + 2 t} t^{3} + 96 e^{- t^{2} + 2 t} t^{2}

Solution steps

- 48 t^{2} e^{- t^{2} + 2 t} (2 t - 2)

= - 48 e^{- t^{2} + 2 t} t^{2} (2 t - 2)

Apply the distributive law:

a (b - c) = ab - a c

a = - 48 t^{2} e^{- t^{2} + 2 t}, b = 2 t, c = 2

= - 48 t^{2} e^{- t^{2} + 2 t} \cdot 2 t - (- 48 t^{2} e^{- t^{2} + 2 t}) \cdot 2

Apply minus-plus rules

- (- a) = a

= - 48 \cdot 2 e^{- t^{2} + 2 t} t^{2} t + 48 \cdot 2 e^{- t^{2} + 2 t} t^{2}

Simplify

- 48 \cdot 2 e^{- t^{2} + 2 t} t^{2} t + 48 \cdot 2 e^{- t^{2} + 2 t} t^{2} : - 96 e^{- t^{2} + 2 t} t^{3} + 96 e^{- t^{2} + 2 t} t^{2}

= - 96 e^{- t^{2} + 2 t} t^{3} + 96 e^{- t^{2} + 2 t} t^{2}

\frac{2 x ^{2} + 8 x - 6}{( x + 2 ) ^{2}}

\frac{2 x ^{3} - 4 x ^{2} - 15 x + 4}{( x - 1 ) ^{2}}

B (2, - 5)

e (1.6784 - 42.2094 ln (x))

4 a - (5) 2

What is expand-48t^2e^{-t^2+2t}*(2t-2) ?
The solution to expand-48t^2e^{-t^2+2t}*(2t-2) is -96e^{-t^2+2t}t^3+96e^{-t^2+2t}t^2