What is expand dx(x^2(1-x)^3) ?

The solution to expand dx(x^2(1-x)^3) is x^2dx-3x^3dx+3x^4dx-x^5dx

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expand dx(x^2(1-x)^3)

expand

d x (x^{2} (1 - x)^{3})

x^{2} d x - 3 x^{3} d x + 3 x^{4} d x - x^{5} d x

Solution steps

d x (x^{2} (1 - x)^{3})

Remove parentheses:

(a) = a

= d x x^{2} (1 - x)^{3}

(1 - x)^{3} = 1 - 3 x + 3 x^{2} - x^{3}

= x^{2} d x (- x^{3} + 3 x^{2} - 3 x + 1)

= x^{2} d x (1 - 3 x + 3 x^{2} - x^{3})

Distribute parentheses

= d x x^{2} \cdot 1 + d x x^{2} (- 3 x) + d x x^{2} \cdot 3 x^{2} + d x x^{2} (- x^{3})

Apply minus-plus rules

+ (- a) = - a

= 1 \cdot x^{2} d x - 3 x^{2} x d x + 3 x^{2} x^{2} d x - x^{3} x^{2} d x

Simplify

1 \cdot x^{2} d x - 3 x^{2} x d x + 3 x^{2} x^{2} d x - x^{3} x^{2} d x : x^{2} d x - 3 x^{3} d x + 3 x^{4} d x - x^{5} d x

= x^{2} d x - 3 x^{3} d x + 3 x^{4} d x - x^{5} d x

(x - 1)^{3} (x + 1) (x + \frac{1}{2})

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

2 (2 x^{2} + y^{2}) d x - x y d y

(x + 2 π)^{4}

- (\frac{8 x}{y} - \frac{w}{t})^{2}

What is expand dx(x^2(1-x)^3) ?
The solution to expand dx(x^2(1-x)^3) is x^2dx-3x^3dx+3x^4dx-x^5dx