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

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

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expand (xe^x-e^x)*(2x-1)

expand

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

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

Solution steps

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

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

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

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

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

Simplify

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

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

\frac{12 s - 3}{( 3 s + 2 ) ^{2}}

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

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

3 (x + δ)^{2}

e^{2 (x + y)}

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