What is expand (e^{-1600t}-e^{-400t})^2 ?

The solution to expand (e^{-1600t}-e^{-400t})^2 is e^{-3200t}-2e^{-2000t}+e^{-800t}

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expand (e^{-1600t}-e^{-400t})^2

expand

(e^{- 1600 t} - e^{- 400 t})^{2}

e^{- 3200 t} - 2 e^{- 2000 t} + e^{- 800 t}

Solution steps

(e^{- 1600 t} - e^{- 400 t})^{2}

Apply Perfect Square Formula:

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

a = e^{- 1600 t}, b = e^{- 400 t}

= (e^{- 1600 t})^{2} - 2 e^{- 1600 t} e^{- 400 t} + (e^{- 400 t})^{2}

Simplify

(e^{- 1600 t})^{2} - 2 e^{- 1600 t} e^{- 400 t} + (e^{- 400 t})^{2} : e^{- 3200 t} - 2 e^{- 2000 t} + e^{- 800 t}

= e^{- 3200 t} - 2 e^{- 2000 t} + e^{- 800 t}

(f \circ g + hk) (x)

(x^{2} + 6 x) cos (x) d x

(y^{'} (x) - 2 y) (2 - 2 x)

ro t a c i o na l (x^{2}, 3 x z^{2}, - 2 x z)

\frac{x ^{2} - 2 x + 1}{( x - 3 ) ( x + 1 )}

What is expand (e^{-1600t}-e^{-400t})^2 ?
The solution to expand (e^{-1600t}-e^{-400t})^2 is e^{-3200t}-2e^{-2000t}+e^{-800t}