What is expand (c_{1}x+c_{2}e^{-2x})e^{2x} ?

The solution to expand (c_{1}x+c_{2}e^{-2x})e^{2x} is c_{1}e^{2x}x+c_{2}

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expand (c_{1}x+c_{2}e^{-2x})e^{2x}

expand

(c_{1} x + c_{2} e^{- 2 x}) e^{2 x}

c_{1} e^{2 x} x + c_{2}

Solution steps

(c_{1} x + c_{2} e^{- 2 x}) e^{2 x}

= e^{2 x} (c_{1} x + c_{2} e^{- 2 x})

Apply the distributive law:

a (b + c) = ab + a c

a = e^{2 x}, b = c_{1} x, c = c_{2} e^{- 2 x}

= e^{2 x} c_{1} x + e^{2 x} c_{2} e^{- 2 x}

= c_{1} e^{2 x} x + c_{2} e^{2 x} e^{- 2 x}

c_{2} e^{2 x} e^{- 2 x} = c_{2}

= c_{1} e^{2 x} x + c_{2}

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What is expand (c_{1}x+c_{2}e^{-2x})e^{2x} ?
The solution to expand (c_{1}x+c_{2}e^{-2x})e^{2x} is c_{1}e^{2x}x+c_{2}