What is expand (3e^{3t}-e^{-t})\times (9e^{6t}+e^{-2t}) ?

The solution to expand (3e^{3t}-e^{-t})\times (9e^{6t}+e^{-2t}) is 27e^{9t}+3e^t-9e^{5t}-e^{-3t}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (3e^{3t}-e^{-t})\times (9e^{6t}+e^{-2t})

expand

(3 e^{3 t} - e^{- t}) \cdot (9 e^{6 t} + e^{- 2 t})

27 e^{9 t} + 3 e^{t} - 9 e^{5 t} - e^{- 3 t}

Solution steps

(3 e^{3 t} - e^{- t}) (9 e^{6 t} + e^{- 2 t})

Apply FOIL method:

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

a = 3 e^{3 t}, b = - e^{- t}, c = 9 e^{6 t}, d = e^{- 2 t}

= 3 e^{3 t} \cdot 9 e^{6 t} + 3 e^{3 t} e^{- 2 t} + (- e^{- t}) \cdot 9 e^{6 t} + (- e^{- t}) e^{- 2 t}

Apply minus-plus rules

+ (- a) = - a

= 3 \cdot 9 e^{3 t} e^{6 t} + 3 e^{3 t} e^{- 2 t} - 9 e^{- t} e^{6 t} - e^{- t} e^{- 2 t}

Simplify

3 \cdot 9 e^{3 t} e^{6 t} + 3 e^{3 t} e^{- 2 t} - 9 e^{- t} e^{6 t} - e^{- t} e^{- 2 t} : 27 e^{9 t} + 3 e^{t} - 9 e^{5 t} - e^{- 3 t}

= 27 e^{9 t} + 3 e^{t} - 9 e^{5 t} - e^{- 3 t}

\frac{s ^{2} + 2 s + 3}{( s ^{2} + 2 s + 2 ) ( s ^{2} + 2 s + 5 )}

A (31, 6) B (- 31, - 2)

2 + 3 - (1 + 2) in

\frac{- s - 1}{( s - 1 ) ( s + 2 )}

6 (\frac{2}{3} - 3 y)

What is expand (3e^{3t}-e^{-t})\times (9e^{6t}+e^{-2t}) ?
The solution to expand (3e^{3t}-e^{-t})\times (9e^{6t}+e^{-2t}) is 27e^{9t}+3e^t-9e^{5t}-e^{-3t}