What is expand x^2(3x^3-2)^4dx ?

The solution to expand x^2(3x^3-2)^4dx is 81x^{14}dx-216x^{11}dx+216x^8dx-96x^5dx+16x^2dx

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expand x^2(3x^3-2)^4dx

expand

x^{2} (3 x^{3} - 2)^{4} d x

81 x^{14} d x - 216 x^{11} d x + 216 x^{8} d x - 96 x^{5} d x + 16 x^{2} d x

Solution steps

x^{2} (3 x^{3} - 2)^{4} d x

(3 x^{3} - 2)^{4} = 81 x^{12} - 216 x^{9} + 216 x^{6} - 96 x^{3} + 16

= x^{2} (81 x^{12} - 216 x^{9} + 216 x^{6} - 96 x^{3} + 16) d x

Distribute parentheses

= x^{2} d x \cdot 81 x^{12} + x^{2} d x (- 216 x^{9}) + x^{2} d x \cdot 216 x^{6} + x^{2} d x (- 96 x^{3}) + x^{2} d x \cdot 16

Apply minus-plus rules

+ (- a) = - a

= 81 x^{12} x^{2} d x - 216 x^{9} x^{2} d x + 216 x^{6} x^{2} d x - 96 x^{3} x^{2} d x + 16 x^{2} d x

Simplify

81 x^{12} x^{2} d x - 216 x^{9} x^{2} d x + 216 x^{6} x^{2} d x - 96 x^{3} x^{2} d x + 16 x^{2} d x : 81 x^{14} d x - 216 x^{11} d x + 216 x^{8} d x - 96 x^{5} d x + 16 x^{2} d x

= 81 x^{14} d x - 216 x^{11} d x + 216 x^{8} d x - 96 x^{5} d x + 16 x^{2} d x

\frac{4}{( x + 1 ) ( x + 5 ) ( s - 3 )}

x^{2} y^{''} (x) + x y^{'} (x) + (x^{2} - \frac{1}{4}) y

\frac{( x - 2 ) ( - 3 x + 180 )}{x}

\frac{( s + 1 )}{( s + 2 ) \cdot ( s + 4 )}

\frac{s + 5}{( s + 4 ) ( s + 1 )}

What is expand x^2(3x^3-2)^4dx ?
The solution to expand x^2(3x^3-2)^4dx is 81x^{14}dx-216x^{11}dx+216x^8dx-96x^5dx+16x^2dx