What is expand t^2(2t^3-5)^4dx ?

The solution to expand t^2(2t^3-5)^4dx is 16t^{14}dx-160t^{11}dx+600t^8dx-1000t^5dx+625t^2dx

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expand t^2(2t^3-5)^4dx

expand

t^{2} (2 t^{3} - 5)^{4} d x

16 t^{14} d x - 160 t^{11} d x + 600 t^{8} d x - 1000 t^{5} d x + 625 t^{2} d x

Solution steps

t^{2} (2 t^{3} - 5)^{4} d x

(2 t^{3} - 5)^{4} = 16 t^{12} - 160 t^{9} + 600 t^{6} - 1000 t^{3} + 625

= t^{2} (16 t^{12} - 160 t^{9} + 600 t^{6} - 1000 t^{3} + 625) d x

Distribute parentheses

= t^{2} d x \cdot 16 t^{12} + t^{2} d x (- 160 t^{9}) + t^{2} d x \cdot 600 t^{6} + t^{2} d x (- 1000 t^{3}) + t^{2} d x \cdot 625

Apply minus-plus rules

+ (- a) = - a

= 16 t^{12} t^{2} d x - 160 t^{9} t^{2} d x + 600 t^{6} t^{2} d x - 1000 t^{3} t^{2} d x + 625 t^{2} d x

Simplify

16 t^{12} t^{2} d x - 160 t^{9} t^{2} d x + 600 t^{6} t^{2} d x - 1000 t^{3} t^{2} d x + 625 t^{2} d x : 16 t^{14} d x - 160 t^{11} d x + 600 t^{8} d x - 1000 t^{5} d x + 625 t^{2} d x

= 16 t^{14} d x - 160 t^{11} d x + 600 t^{8} d x - 1000 t^{5} d x + 625 t^{2} d x

(2 + t) (9 - t^{2})

\frac{d ^{2}}{d x ^{2}} ((y) (x^{2} + y^{2}))

(m y - p) (m^{2} y^{2} +, + p^{2})

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

What is expand t^2(2t^3-5)^4dx ?
The solution to expand t^2(2t^3-5)^4dx is 16t^{14}dx-160t^{11}dx+600t^8dx-1000t^5dx+625t^2dx