What is expand (10e^{-t}-5e^{-2t})^2 ?

The solution to expand (10e^{-t}-5e^{-2t})^2 is 100e^{-2t}-100e^{-3t}+25e^{-4t}

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expand (10e^{-t}-5e^{-2t})^2

expand

(10 e^{- t} - 5 e^{- 2 t})^{2}

100 e^{- 2 t} - 100 e^{- 3 t} + 25 e^{- 4 t}

Solution steps

(10 e^{- t} - 5 e^{- 2 t})^{2}

Apply Perfect Square Formula:

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

a = 10 e^{- t}, b = 5 e^{- 2 t}

= (10 e^{- t})^{2} - 2 \cdot 10 e^{- t} \cdot 5 e^{- 2 t} + (5 e^{- 2 t})^{2}

Simplify

(10 e^{- t})^{2} - 2 \cdot 10 e^{- t} \cdot 5 e^{- 2 t} + (5 e^{- 2 t})^{2} : 100 e^{- 2 t} - 100 e^{- 3 t} + 25 e^{- 4 t}

= 100 e^{- 2 t} - 100 e^{- 3 t} + 25 e^{- 4 t}

(\frac{x}{2 - 5 y}) 4

(x - x x) (x - 1)

\frac{( D s ^{2} + P s + I ) \cdot 4865}{s ( s ^{2} + 497.8 s + 5951 )}

(4 + x 2)^{2}

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

What is expand (10e^{-t}-5e^{-2t})^2 ?
The solution to expand (10e^{-t}-5e^{-2t})^2 is 100e^{-2t}-100e^{-3t}+25e^{-4t}