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

The solution to expand (e^{2x})(e^xx+e^x-2e^{-2x}C) is e^{3x}x+e^{3x}-2C

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expand (e^{2x})(e^xx+e^x-2e^{-2x}C)

expand

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

e^{3 x} x + e^{3 x} - 2 C

Solution steps

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

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

Simplify

e^{x} x (e^{2 x}) + e^{x} (e^{2 x}) - 2 e^{- 2 x} C (e^{2 x}) : e^{3 x} x + e^{3 x} - 2 C

= e^{3 x} x + e^{3 x} - 2 C

(\frac{80 - p}{2}) \cdot (p - w)

25 y^{6} + (y^{8} - 5)^{2}

\frac{s ^{2} + s + 1}{s ^{2} ( s ^{2} - 2 s + 10 )}

(e^{x}) (6 x) + (3 x^{2} + 5) (e^{x})

24 (x cos (θ) - y sin (θ)) (x sin (θ) + y cos (θ))

What is expand (e^{2x})(e^xx+e^x-2e^{-2x}C) ?
The solution to expand (e^{2x})(e^xx+e^x-2e^{-2x}C) is e^{3x}x+e^{3x}-2C