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

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

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expand (e^{-x^2}-2e^{-x^2}x^2)^2

expand

(e^{- x^{2}} - 2 e^{- x^{2}} x^{2})^{2}

e^{- 2 x^{2}} - 4 e^{- 2 x^{2}} x^{2} + 4 e^{- 2 x^{2}} x^{4}

Solution steps

(e^{- x^{2}} - 2 e^{- x^{2}} x^{2})^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

= e^{- 2 x^{2}} - 4 e^{- 2 x^{2}} x^{2} + 4 e^{- 2 x^{2}} x^{4}

(f \circ g) (2 x^{2} + x)

\frac{( 4 x + 1 ) ^{2}}{( x - 2 ) ( x + 3 )}

d x [x (5 x^{4} - 7 x^{2} - 3)]

sin (\frac{x}{2}) (2 sin (\frac{x}{2}) - 1)

(y + 1) e^{x}

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