What is expand 2(4e^{-2x}x^3-2e^{-2x}x^4) ?

The solution to expand 2(4e^{-2x}x^3-2e^{-2x}x^4) is 8e^{-2x}x^3-4e^{-2x}x^4

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expand 2(4e^{-2x}x^3-2e^{-2x}x^4)

expand

2 (4 e^{- 2 x} x^{3} - 2 e^{- 2 x} x^{4})

8 e^{- 2 x} x^{3} - 4 e^{- 2 x} x^{4}

Solution steps

2 (4 e^{- 2 x} x^{3} - 2 e^{- 2 x} x^{4})

Apply the distributive law:

a (b - c) = ab - a c

a = 2, b = 4 e^{- 2 x} x^{3}, c = 2 e^{- 2 x} x^{4}

= 2 \cdot 4 e^{- 2 x} x^{3} - 2 \cdot 2 e^{- 2 x} x^{4}

Simplify

2 \cdot 4 e^{- 2 x} x^{3} - 2 \cdot 2 e^{- 2 x} x^{4} : 8 e^{- 2 x} x^{3} - 4 e^{- 2 x} x^{4}

= 8 e^{- 2 x} x^{3} - 4 e^{- 2 x} x^{4}

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

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

(2 + i) e^{- ik t}

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

\frac{2 x - 7}{( 2 x - 1 ) ( 3 x - 1 )}

What is expand 2(4e^{-2x}x^3-2e^{-2x}x^4) ?
The solution to expand 2(4e^{-2x}x^3-2e^{-2x}x^4) is 8e^{-2x}x^3-4e^{-2x}x^4