What is expand te^{xt}(e^{jbt}+e^{-jbt}) ?

The solution to expand te^{xt}(e^{jbt}+e^{-jbt}) is e^{tx+bjt}t+e^{tx-bjt}t

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expand te^{xt}(e^{jbt}+e^{-jbt})

expand

t e^{x t} (e^{jb t} + e^{- jb t})

e^{t x + bj t} t + e^{t x - bj t} t

Solution steps

t e^{x t} (e^{jb t} + e^{- jb t})

= e^{t x} t (e^{bj t} + e^{- bj t})

Apply the distributive law:

a (b + c) = ab + a c

a = t e^{x t}, b = e^{jb t}, c = e^{- jb t}

= t e^{x t} e^{jb t} + t e^{x t} e^{- jb t}

= e^{t x} e^{bj t} t + e^{t x} e^{- bj t} t

Simplify

e^{t x} e^{bj t} t + e^{t x} e^{- bj t} t : e^{t x + bj t} t + e^{t x - bj t} t

= e^{t x + bj t} t + e^{t x - bj t} t

\frac{( x + 2 ) ^{2}}{20 ( y - 5 )}

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

4 (m = \frac{3}{4} n - v)

- 8 - 3 (w + 13 = 4 (w + 11)) - 7 w

\frac{x ^{6}}{x ^{5}}

What is expand te^{xt}(e^{jbt}+e^{-jbt}) ?
The solution to expand te^{xt}(e^{jbt}+e^{-jbt}) is e^{tx+bjt}t+e^{tx-bjt}t