What is expand (5e^{5t}-e^{-t})*(25e^{5t}+e^{-t}) ?

The solution to expand (5e^{5t}-e^{-t})*(25e^{5t}+e^{-t}) is 125e^{10t}-20e^{4t}-e^{-2t}

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expand (5e^{5t}-e^{-t})*(25e^{5t}+e^{-t})

expand

(5 e^{5 t} - e^{- t}) \cdot (25 e^{5 t} + e^{- t})

125 e^{10 t} - 20 e^{4 t} - e^{- 2 t}

Solution steps

(5 e^{5 t} - e^{- t}) (25 e^{5 t} + e^{- t})

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = 5 e^{5 t}, b = - e^{- t}, c = 25 e^{5 t}, d = e^{- t}

= 5 e^{5 t} \cdot 25 e^{5 t} + 5 e^{5 t} e^{- t} + (- e^{- t}) \cdot 25 e^{5 t} + (- e^{- t}) e^{- t}

Apply minus-plus rules

+ (- a) = - a

= 5 \cdot 25 e^{5 t} e^{5 t} + 5 e^{5 t} e^{- t} - 25 e^{- t} e^{5 t} - e^{- t} e^{- t}

Simplify

5 \cdot 25 e^{5 t} e^{5 t} + 5 e^{5 t} e^{- t} - 25 e^{- t} e^{5 t} - e^{- t} e^{- t} : 125 e^{10 t} - 20 e^{4 t} - e^{- 2 t}

= 125 e^{10 t} - 20 e^{4 t} - e^{- 2 t}

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\frac{d}{d x} ((L (x)) 2) - \frac{2}{( x + 1 ) ^{2}}

- \frac{144 ( - x ^{2} + 4 )}{( x ^{2} + 12 ) ^{3}}

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What is expand (5e^{5t}-e^{-t})*(25e^{5t}+e^{-t}) ?
The solution to expand (5e^{5t}-e^{-t})*(25e^{5t}+e^{-t}) is 125e^{10t}-20e^{4t}-e^{-2t}