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

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

Popular >

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

r^{3} \cdot cos (y) sin (y) (4 - r^{2})

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

(2 x - 1) (x - 2) (x - 3) (x - 4 - i) (x - 4 + i)

4 x (5 x - 1)

\frac{- 3 h ^{2} - 8 h}{8 ( h + 4 ) ^{2}}

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