What is expand f((te^{at})/a+(-e^{at}+1)/(a^2)) ?

The solution to expand f((te^{at})/a+(-e^{at}+1)/(a^2)) is (e^{ta}ft)/a-(e^{ta}f)/(a^2)+f/(a^2)

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expand f((te^{at})/a+(-e^{at}+1)/(a^2))

expand

f (\frac{t e ^{a t}}{a} + \frac{- e ^{a t} + 1}{a ^{2}})

\frac{e ^{t a} f t}{a} - \frac{e ^{t a} f}{a ^{2}} + \frac{f}{a ^{2}}

Solution steps

f (\frac{t e ^{a t}}{a} + \frac{- e ^{a t} + 1}{a ^{2}})

= f (\frac{e ^{t a} t}{a} + \frac{- e ^{t a} + 1}{a ^{2}})

Apply the distributive law:

a (b + c) = ab + a c

a = f, b = \frac{t e ^{a t}}{a}, c = \frac{- e ^{a t} + 1}{a ^{2}}

= f \frac{t e ^{a t}}{a} + f \frac{- e ^{a t} + 1}{a ^{2}}

= \frac{e ^{t a} t}{a} f + \frac{- e ^{t a} + 1}{a ^{2}} f

Simplify

\frac{e ^{t a} t}{a} f + \frac{- e ^{t a} + 1}{a ^{2}} f : \frac{e ^{t a} f t}{a} - \frac{e ^{t a} f}{a ^{2}} + \frac{f}{a ^{2}}

= \frac{e ^{t a} f t}{a} - \frac{e ^{t a} f}{a ^{2}} + \frac{f}{a ^{2}}

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\frac{6}{x ( 6 - x )}

(e^{3 x i} - e^{- 3 x i})^{2}

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

What is expand f((te^{at})/a+(-e^{at}+1)/(a^2)) ?
The solution to expand f((te^{at})/a+(-e^{at}+1)/(a^2)) is (e^{ta}ft)/a-(e^{ta}f)/(a^2)+f/(a^2)