What is expand x^2(x-9)^5dx ?

The solution to expand x^2(x-9)^5dx is x^7dx-45x^6dx+810x^5dx-7290x^4dx+32805x^3dx-59049x^2dx

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expand x^2(x-9)^5dx

expand

x^{2} (x - 9)^{5} d x

x^{7} d x - 45 x^{6} d x + 810 x^{5} d x - 7290 x^{4} d x + 32805 x^{3} d x - 59049 x^{2} d x

Solution steps

x^{2} (x - 9)^{5} d x

(x - 9)^{5} = x^{5} - 45 x^{4} + 810 x^{3} - 7290 x^{2} + 32805 x - 59049

= x^{2} (x^{5} - 45 x^{4} + 810 x^{3} - 7290 x^{2} + 32805 x - 59049) d x

Distribute parentheses

= x^{2} d x x^{5} + x^{2} d x (- 45 x^{4}) + x^{2} d x \cdot 810 x^{3} + x^{2} d x (- 7290 x^{2}) + x^{2} d x \cdot 32805 x + x^{2} d x (- 59049)

Apply minus-plus rules

+ (- a) = - a

= x^{5} x^{2} d x - 45 x^{4} x^{2} d x + 810 x^{3} x^{2} d x - 7290 x^{2} x^{2} d x + 32805 x^{2} x d x - 59049 x^{2} d x

Simplify

x^{5} x^{2} d x - 45 x^{4} x^{2} d x + 810 x^{3} x^{2} d x - 7290 x^{2} x^{2} d x + 32805 x^{2} x d x - 59049 x^{2} d x : x^{7} d x - 45 x^{6} d x + 810 x^{5} d x - 7290 x^{4} d x + 32805 x^{3} d x - 59049 x^{2} d x

= x^{7} d x - 45 x^{6} d x + 810 x^{5} d x - 7290 x^{4} d x + 32805 x^{3} d x - 59049 x^{2} d x

[(t + 1)^{2} + e^{t - 2}] U (t - 2)

(D + x) (D + 1) e^{x}

(1 + i)^{5}

(3 + i)^{26}

(e^{u} + e^{- u}) (e^{u} - e^{- u})

What is expand x^2(x-9)^5dx ?
The solution to expand x^2(x-9)^5dx is x^7dx-45x^6dx+810x^5dx-7290x^4dx+32805x^3dx-59049x^2dx