What is expand (e^{-t}t^2(14+2t))/9+15-10t ?

The solution to expand (e^{-t}t^2(14+2t))/9+15-10t is (14e^{-t}t^2)/9+(2e^{-t}t^3)/9+15-10t

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expand (e^{-t}t^2(14+2t))/9+15-10t

expand

\frac{e ^{- t} t ^{2} ( 14 + 2 t )}{9} + 15 - 10 t

\frac{14 e ^{- t} t ^{2}}{9} + \frac{2 e ^{- t} t ^{3}}{9} + 15 - 10 t

Solution steps

\frac{e ^{- t} t ^{2} ( 14 + 2 t )}{9} + 15 - 10 t

Expand

e^{- t} t^{2} (14 + 2 t) : 14 e^{- t} t^{2} + 2 e^{- t} t^{3}

= \frac{2 e ^{- t} t ^{3} + 14 e ^{- t} t ^{2}}{9} + 15 - 10 t

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{14 e ^{- t} t ^{2} + 2 e ^{- t} t ^{3}}{9} = \frac{14 e ^{- t} t ^{2}}{9} + \frac{2 e ^{- t} t ^{3}}{9}

= \frac{14 e ^{- t} t ^{2}}{9} + \frac{2 e ^{- t} t ^{3}}{9} + 15 - 10 t

(\frac{3 x ^{3}}{2} + 9 y^{2}) (\frac{3 x ^{3}}{2} - 9 y^{2})

(x + 1) (x - 4) (x - 2)

(\frac{A}{6} + 4 Z) (A - 5 Z)

(- x^{2} + 8 \circ 4 x + 8) (- 4)

z (- x_{1} + x_{2} - 4)^{2}

What is expand (e^{-t}t^2(14+2t))/9+15-10t ?
The solution to expand (e^{-t}t^2(14+2t))/9+15-10t is (14e^{-t}t^2)/9+(2e^{-t}t^3)/9+15-10t