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

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

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

expand

(1 - c e^{- \frac{x ^{2}}{2}})^{2}

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

Solution steps

(1 - c e^{- \frac{x ^{2}}{2}})^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

\frac{( 1 + r ) ( 1 - a ) ( x ) + c}{( 1 + r )}

2 x^{2} - x^{- 1}

y^{2} (e^{x y} + e^{x y} x y)

\frac{( s - 1 )}{( s - 2 ) ( s - 3 )}

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

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