What is expand (e^{-2x}+1)^3 ?

The solution to expand (e^{-2x}+1)^3 is e^{-6x}+3e^{-4x}+3e^{-2x}+1

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expand (e^{-2x}+1)^3

expand

(e^{- 2 x} + 1)^{3}

e^{- 6 x} + 3 e^{- 4 x} + 3 e^{- 2 x} + 1

Solution steps

(e^{- 2 x} + 1)^{3}

Apply Perfect Cube Formula:

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

a = e^{- 2 x}, b = 1

= (e^{- 2 x})^{3} + 3 (e^{- 2 x})^{2} \cdot 1 + 3 e^{- 2 x} \cdot 1^{2} + 1^{3}

Simplify

(e^{- 2 x})^{3} + 3 (e^{- 2 x})^{2} \cdot 1 + 3 e^{- 2 x} \cdot 1^{2} + 1^{3} : e^{- 6 x} + 3 e^{- 4 x} + 3 e^{- 2 x} + 1

= e^{- 6 x} + 3 e^{- 4 x} + 3 e^{- 2 x} + 1

(x + y = 6,) - (x + 2 y = 7)

\frac{144 ( r + 144 )}{r}

\frac{a}{s ^{2} ( a s + C )}

(2 + j) e^{j^{9} t} + (2 - j) e^{- 9 t}

, (x^{2} + y^{2} = 25)

What is expand (e^{-2x}+1)^3 ?
The solution to expand (e^{-2x}+1)^3 is e^{-6x}+3e^{-4x}+3e^{-2x}+1