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

The solution to expand (1+ce^{-x})^2 is 1+2ce^{-x}+c^2e^{-2x}

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expand (1+ce^{-x})^2

expand

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

1 + 2 c e^{- x} + c^{2} e^{- 2 x}

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

1^{2} + 2 \cdot 1 \cdot c e^{- x} + (c e^{- x})^{2} : 1 + 2 c e^{- x} + c^{2} e^{- 2 x}

= 1 + 2 c e^{- x} + c^{2} e^{- 2 x}

\frac{1}{( x + 4 ) ( x - 2 )}

\frac{1}{( x + 1 ) ( 3 x + 1 ) ( 6 x + 3 )}

\frac{8 x ^{2} + 12 x}{( 3 x - 2 ) ^{2}}

\frac{d}{d y} ((x) (x^{2} - 7))

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

What is expand (1+ce^{-x})^2 ?
The solution to expand (1+ce^{-x})^2 is 1+2ce^{-x}+c^2e^{-2x}