What is expand-2a(-2ae^{-ax^2}x^2+e^{-ax^2}) ?

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

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expand-2a(-2ae^{-ax^2}x^2+e^{-ax^2})

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

= - 2 a (- 2 a e^{- a x^{2}} x^{2}) + (- 2 a) e^{- a x^{2}}

Apply minus-plus rules

- (- a) = a, + (- a) = - a

= 2 \cdot 2 aa e^{- a x^{2}} x^{2} - 2 a e^{- a x^{2}}

2 \cdot 2 aa e^{- a x^{2}} x^{2} = 4 a^{2} e^{- a x^{2}} x^{2}

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

(e^{u} + e^{- u})^{2}

(2 - 1 1)

d (1 - cos (u))

\frac{6 c ^{2}}{5 d ^{3} ( t ^{2} - 8 t ^{3} ) ^{6}}

(6 - x)^{2}

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