What is expand a(e^{-ka^2}-2ke^{-ka^2}a^2) ?

The solution to expand a(e^{-ka^2}-2ke^{-ka^2}a^2) is ae^{-a^2k}-2a^3e^{-a^2k}k

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expand a(e^{-ka^2}-2ke^{-ka^2}a^2)

expand

a (e^{- k a^{2}} - 2 k e^{- k a^{2}} a^{2})

a e^{- a^{2} k} - 2 a^{3} e^{- a^{2} k} k

Solution steps

a (e^{- k a^{2}} - 2 k e^{- k a^{2}} a^{2})

= a (e^{- a^{2} k} - 2 a^{2} e^{- a^{2} k} k)

Apply the distributive law:

a (b - c) = ab - a c

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

= a e^{- k a^{2}} - a \cdot 2 k e^{- k a^{2}} a^{2}

= a e^{- a^{2} k} - 2 a^{2} a e^{- a^{2} k} k

2 a^{2} a e^{- a^{2} k} k = 2 a^{3} e^{- a^{2} k} k

= a e^{- a^{2} k} - 2 a^{3} e^{- a^{2} k} k

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(- 1 + 6 x) - 7 + 5

(\frac{3}{e ^{q}} + 10) \cdot q

(P (R - 1) + R)^{X} \cdot R^{1 - X}

\frac{3 ( 2 x ^{2} + 10 x + 11 )}{2}

What is expand a(e^{-ka^2}-2ke^{-ka^2}a^2) ?
The solution to expand a(e^{-ka^2}-2ke^{-ka^2}a^2) is ae^{-a^2k}-2a^3e^{-a^2k}k