What is expand (xe^x-e^x+C)(2x-1) ?

The solution to expand (xe^x-e^x+C)(2x-1) is 2e^xx^2-3e^xx+e^x+2xC-C

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expand (xe^x-e^x+C)(2x-1)

expand

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

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

Solution steps

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

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

Distribute parentheses

= x e^{x} \cdot 2 x + x e^{x} (- 1) + (- e^{x}) \cdot 2 x + (- e^{x}) (- 1) + C \cdot 2 x + C (- 1)

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= 2 e^{x} xx - 1 \cdot e^{x} x - 2 e^{x} x + 1 \cdot e^{x} + 2 x C - 1 \cdot C

Simplify

2 e^{x} xx - 1 \cdot e^{x} x - 2 e^{x} x + 1 \cdot e^{x} + 2 x C - 1 \cdot C : 2 e^{x} x^{2} - 3 e^{x} x + e^{x} + 2 x C - C

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

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

\frac{d x}{x ^{2} ( x ^{2} + 4 )}

A (10, 5) B (3, 2) C (6, - 5)

\frac{5 + ( - 6 ) 3}{3}

(13 x^{2} - 29 x - 227) e^{3} x + C

What is expand (xe^x-e^x+C)(2x-1) ?
The solution to expand (xe^x-e^x+C)(2x-1) is 2e^xx^2-3e^xx+e^x+2xC-C