What is expand 3((3e^{-t}t^2)/2-6e^{-t}t+3e^{-t}) ?

The solution to expand 3((3e^{-t}t^2)/2-6e^{-t}t+3e^{-t}) is (9e^{-t}t^2)/2-18e^{-t}t+9e^{-t}

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expand 3((3e^{-t}t^2)/2-6e^{-t}t+3e^{-t})

expand

3 (\frac{3 e ^{- t} t ^{2}}{2} - 6 e^{- t} t + 3 e^{- t})

\frac{9 e ^{- t} t ^{2}}{2} - 18 e^{- t} t + 9 e^{- t}

Solution steps

3 (\frac{3 e ^{- t} t ^{2}}{2} - 6 e^{- t} t + 3 e^{- t})

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

= 3 \cdot \frac{3 e ^{- t} t ^{2}}{2} - 3 \cdot 6 e^{- t} t + 3 \cdot 3 e^{- t}

Simplify

3 \cdot \frac{3 e ^{- t} t ^{2}}{2} - 3 \cdot 6 e^{- t} t + 3 \cdot 3 e^{- t} : \frac{9 e ^{- t} t ^{2}}{2} - 18 e^{- t} t + 9 e^{- t}

= \frac{9 e ^{- t} t ^{2}}{2} - 18 e^{- t} t + 9 e^{- t}

\frac{e ^{- x} - x ^{2} - x + 10}{( x - 1 ) ( x + 4 ) ( x - 2 )}

(x + sin (\frac{π \cdot x}{2})) \cdot (x + cos (\frac{π \cdot x}{2}))^{2}

\frac{10 ( 3 191 - 2 )}{49}

lo g_{10} (y)

\frac{\partial}{\partial x} ((y) (x^{2} + x y - 10))

What is expand 3((3e^{-t}t^2)/2-6e^{-t}t+3e^{-t}) ?
The solution to expand 3((3e^{-t}t^2)/2-6e^{-t}t+3e^{-t}) is (9e^{-t}t^2)/2-18e^{-t}t+9e^{-t}