What is expand (e^{-t}-te^{-t})^2 ?

The solution to expand (e^{-t}-te^{-t})^2 is e^{-2t}-2e^{-2t}t+e^{-2t}t^2

Popular >

expand (e^{-t}-te^{-t})^2

expand

(e^{- t} - t e^{- t})^{2}

e^{- 2 t} - 2 e^{- 2 t} t + e^{- 2 t} t^{2}

Solution steps

(e^{- t} - t e^{- t})^{2}

= (e^{- t} - e^{- t} t)^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

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

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

Simplify

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

= e^{- 2 t} - 2 e^{- 2 t} t + e^{- 2 t} t^{2}

(2 - 5 x)^{2}

(x + 1 + 2) (x + 1 - 2)

\frac{d}{d x} ((z) (2 x y z - e^{z}))

(- \frac{b}{a} y - \frac{c}{a} z + d)^{2} + y^{2} - z^{2}

5 (3 b^{2} + 4 b - 6)^{2}

What is expand (e^{-t}-te^{-t})^2 ?
The solution to expand (e^{-t}-te^{-t})^2 is e^{-2t}-2e^{-2t}t+e^{-2t}t^2