What is expand (3x-2)(3x^2-4x+25)^5dx ?

The solution to expand (3x-2)(3x^2-4x+25)^5dx is

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expand (3x-2)(3x^2-4x+25)^5dx

expand

(3 x - 2) (3 x^{2} - 4 x + 25)^{5} d x

729 x^{11} d x - 5346 x^{10} d x + 46575 x^{9} d x - 208170 x^{8} d x + 961290 x^{7} d x - 2877252 x^{6} d x + 8558798 x^{5} d x - 17126500 x^{4} d x + 33378125 x^{3} d x - 40156250 x^{2} d x + 44921875 x d x - 19531250 d x

Solution steps

(3 x - 2) (3 x^{2} - 4 x + 25)^{5} d x

Apply the distributive law:

a (b - c) = ab - a c

a = (3 x^{2} - 4 x + 25)^{5} d x, b = 3 x, c = 2

= (3 x^{2} - 4 x + 25)^{5} d x \cdot 3 x - (3 x^{2} - 4 x + 25)^{5} d x \cdot 2

= 3 x (3 x^{2} - 4 x + 25)^{5} d x - 2 (3 x^{2} - 4 x + 25)^{5} d x

Simplify

3 x (3 x^{2} - 4 x + 25)^{5} d x - 2 (3 x^{2} - 4 x + 25)^{5} d x : 729 x^{11} d x - 5346 x^{10} d x + 46575 x^{9} d x - 208170 x^{8} d x + 961290 x^{7} d x - 2877252 x^{6} d x + 8558798 x^{5} d x - 17126500 x^{4} d x + 33378125 x^{3} d x - 40156250 x^{2} d x + 44921875 x d x - 19531250 d x

= 729 x^{11} d x - 5346 x^{10} d x + 46575 x^{9} d x - 208170 x^{8} d x + 961290 x^{7} d x - 2877252 x^{6} d x + 8558798 x^{5} d x - 17126500 x^{4} d x + 33378125 x^{3} d x - 40156250 x^{2} d x + 44921875 x d x - 19531250 d x

lo g_{10} (b) (z^{5} x)

cosh (t) U (t - 3)

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

2 (3 π - \frac{9 3}{4})

\frac{5 e ^{- 5 s} + 2 s}{( s ^{2} + 1 ) ( s )}

What is expand (3x-2)(3x^2-4x+25)^5dx ?
The solution to expand (3x-2)(3x^2-4x+25)^5dx is