What is expand x(x^2-1)^3dz ?

The solution to expand x(x^2-1)^3dz is x^7dz-3x^5dz+3x^3dz-xdz

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expand x(x^2-1)^3dz

expand

x (x^{2} - 1)^{3} d z

x^{7} d z - 3 x^{5} d z + 3 x^{3} d z - x d z

Solution steps

x (x^{2} - 1)^{3} d z

(x^{2} - 1)^{3} = x^{6} - 3 x^{4} + 3 x^{2} - 1

= x (x^{6} - 3 x^{4} + 3 x^{2} - 1) d z

Distribute parentheses

= x d z x^{6} + x d z (- 3 x^{4}) + x d z \cdot 3 x^{2} + x d z (- 1)

Apply minus-plus rules

+ (- a) = - a

= x^{6} x d z - 3 x^{4} x d z + 3 x^{2} x d z - 1 \cdot x d z

Simplify

x^{6} x d z - 3 x^{4} x d z + 3 x^{2} x d z - 1 \cdot x d z : x^{7} d z - 3 x^{5} d z + 3 x^{3} d z - x d z

= x^{7} d z - 3 x^{5} d z + 3 x^{3} d z - x d z

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What is expand x(x^2-1)^3dz ?
The solution to expand x(x^2-1)^3dz is x^7dz-3x^5dz+3x^3dz-xdz