What is expand (x^2-7)^4(2x)dx ?

The solution to expand (x^2-7)^4(2x)dx is 2x^9dx-56x^7dx+588x^5dx-2744x^3dx+4802xdx

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expand (x^2-7)^4(2x)dx

expand

(x^{2} - 7)^{4} (2 x) d x

2 x^{9} d x - 56 x^{7} d x + 588 x^{5} d x - 2744 x^{3} d x + 4802 x d x

Solution steps

(x^{2} - 7)^{4} (2 x) d x

Remove parentheses:

(a) = a

= (x^{2} - 7)^{4} \cdot 2 x d x

(x^{2} - 7)^{4} = x^{8} - 28 x^{6} + 294 x^{4} - 1372 x^{2} + 2401

= 2 x (x^{8} - 28 x^{6} + 294 x^{4} - 1372 x^{2} + 2401) d x

= 2 x (x^{8} - 28 x^{6} + 294 x^{4} - 1372 x^{2} + 2401) d x

Distribute parentheses

= 2 x d x x^{8} + 2 x d x (- 28 x^{6}) + 2 x d x \cdot 294 x^{4} + 2 x d x (- 1372 x^{2}) + 2 x d x \cdot 2401

Apply minus-plus rules

+ (- a) = - a

= 2 x^{8} x d x - 2 \cdot 28 x^{6} x d x + 2 \cdot 294 x^{4} x d x - 2 \cdot 1372 x^{2} x d x + 2 \cdot 2401 x d x

Simplify

2 x^{8} x d x - 2 \cdot 28 x^{6} x d x + 2 \cdot 294 x^{4} x d x - 2 \cdot 1372 x^{2} x d x + 2 \cdot 2401 x d x : 2 x^{9} d x - 56 x^{7} d x + 588 x^{5} d x - 2744 x^{3} d x + 4802 x d x

= 2 x^{9} d x - 56 x^{7} d x + 588 x^{5} d x - 2744 x^{3} d x + 4802 x d x

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What is expand (x^2-7)^4(2x)dx ?
The solution to expand (x^2-7)^4(2x)dx is 2x^9dx-56x^7dx+588x^5dx-2744x^3dx+4802xdx