en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (e^{jt}+e^{-jt})^3

Solution

expand

(e^{j t} + e^{- j t})^{3}

Solution

e^{3 j t} + 3 e^{j t} + 3 e^{- j t} + e^{- 3 j t}

Solution steps

(e^{j t} + e^{- j t})^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

a = e^{j t}, b = e^{- j t}

= (e^{j t})^{3} + 3 (e^{j t})^{2} e^{- j t} + 3 e^{j t} (e^{- j t})^{2} + (e^{- j t})^{3}

Simplify

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

= e^{3 j t} + 3 e^{j t} + 3 e^{- j t} + e^{- 3 j t}

Popular Examples

expand ((\sqrt[3]{r}+1)^3)/(14\sqrt[4]{r)+1}expand

expand 15(1-e^{-0.04t})expand

15 (1 - e^{- 0.04 t})

d/(dt)((θ)(2e^{2t}-4e^{3t}))

\frac{d}{d t} ((θ) (2 e^{2 t} - 4 e^{3 t}))

expand 1/(s^2(s+3))expand

\frac{1}{s ^{2} ( s + 3 )}

expand-(x^3+3y^2)dy expand

- (x^{3} + 3 y^{2}) d y

Frequently Asked Questions (FAQ)

What is expand (e^{jt}+e^{-jt})^3 ?
The solution to expand (e^{jt}+e^{-jt})^3 is e^{3jt}+3e^{jt}+3e^{-jt}+e^{-3jt}