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

The solution to expand (D^2+2D-3)(4e^{2x}) is 4D^2e^{2x}+8De^{2x}-12e^{2x}

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

expand

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

4 D^{2} e^{2 x} + 8 D e^{2 x} - 12 e^{2 x}

Solution steps

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

Distribute parentheses

= (4 e^{2 x}) D^{2} + (4 e^{2 x}) \cdot 2 D + (4 e^{2 x}) (- 3)

Apply minus-plus rules

+ (- a) = - a

= D^{2} (4 e^{2 x}) + 2 D (4 e^{2 x}) - 3 (4 e^{2 x})

Simplify

D^{2} (4 e^{2 x}) + 2 D (4 e^{2 x}) - 3 (4 e^{2 x}) : 4 D^{2} e^{2 x} + 8 D e^{2 x} - 12 e^{2 x}

= 4 D^{2} e^{2 x} + 8 D e^{2 x} - 12 e^{2 x}

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

e^{t} cos (t) U (t - 1)

2 (ln (x) + 1)

\frac{x + 1 - a}{( x + 1 ) ( x - 1 )}

(- e^{- x}) (2 - sin (2 x))

What is expand (D^2+2D-3)(4e^{2x}) ?
The solution to expand (D^2+2D-3)(4e^{2x}) is 4D^2e^{2x}+8De^{2x}-12e^{2x}