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

The solution to expand x(2x-1)^2e^x is 4e^xx^3-4e^xx^2+e^xx

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

expand

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

4 e^{x} x^{3} - 4 e^{x} x^{2} + e^{x} x

Solution steps

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

(2 x - 1)^{2} = 4 x^{2} - 4 x + 1

= e^{x} x (4 x^{2} - 4 x + 1)

= e^{x} x (4 x^{2} - 4 x + 1)

Distribute parentheses

= x e^{x} \cdot 4 x^{2} + x e^{x} (- 4 x) + x e^{x} \cdot 1

Apply minus-plus rules

+ (- a) = - a

= 4 e^{x} x^{2} x - 4 e^{x} xx + 1 \cdot e^{x} x

Simplify

4 e^{x} x^{2} x - 4 e^{x} xx + 1 \cdot e^{x} x : 4 e^{x} x^{3} - 4 e^{x} x^{2} + e^{x} x

= 4 e^{x} x^{3} - 4 e^{x} x^{2} + e^{x} x

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What is expand x(2x-1)^2e^x ?
The solution to expand x(2x-1)^2e^x is 4e^xx^3-4e^xx^2+e^xx