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

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

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

expand

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

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

Solution steps

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

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

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

Distribute parentheses

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

(e^{x} + e^{6})^{2}

\frac{s}{( s + 1 ) \cdot ( s + 2 )}

5 (x^{2} \cdot \frac{x}{5} \cdot \frac{3}{4})

(3 e^{3 x + 1} + e)^{4}

(4)^{\frac{1}{2}} - (4)^{\frac{1}{2}}

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