What is expand (x^2-2x+2)(x^2-2)(x^2+2x+2)(x^2+2) ?

The solution to expand (x^2-2x+2)(x^2-2)(x^2+2x+2)(x^2+2) is x^8-16

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expand (x^2-2x+2)(x^2-2)(x^2+2x+2)(x^2+2)

expand

(x^{2} - 2 x + 2) (x^{2} - 2) (x^{2} + 2 x + 2) (x^{2} + 2)

x^{8} - 16

Solution steps

(x^{2} - 2 x + 2) (x^{2} - 2) (x^{2} + 2 x + 2) (x^{2} + 2)

Expand

(x^{2} - 2 x + 2) (x^{2} - 2) (x^{2} + 2 x + 2) (x^{2} + 2) : (x^{2} - 2 x + 2) (x^{4} - 4) (x^{2} + 2 x + 2)

= (x^{2} - 2 x + 2) (x^{4} - 4) (x^{2} + 2 x + 2)

Expand

(x^{2} - 2 x + 2) (x^{4} - 4) : x^{6} - 4 x^{2} - 2 x^{5} + 8 x + 2 x^{4} - 8

= (x^{6} - 4 x^{2} - 2 x^{5} + 8 x + 2 x^{4} - 8) (x^{2} + 2 x + 2)

Distribute parentheses

= x^{6} x^{2} + x^{6} \cdot 2 x + x^{6} \cdot 2 - 4 x^{2} x^{2} - 4 x^{2} \cdot 2 x - 4 x^{2} \cdot 2 - 2 x^{5} x^{2} - 2 x^{5} \cdot 2 x - 2 x^{5} \cdot 2 + 8 x x^{2} + 8 x \cdot 2 x + 8 x \cdot 2 + 2 x^{4} x^{2} + 2 x^{4} \cdot 2 x + 2 x^{4} \cdot 2 - 8 x^{2} - 8 \cdot 2 x - 8 \cdot 2

Simplify

x^{6} x^{2} + x^{6} \cdot 2 x + x^{6} \cdot 2 - 4 x^{2} x^{2} - 4 x^{2} \cdot 2 x - 4 x^{2} \cdot 2 - 2 x^{5} x^{2} - 2 x^{5} \cdot 2 x - 2 x^{5} \cdot 2 + 8 x x^{2} + 8 x \cdot 2 x + 8 x \cdot 2 + 2 x^{4} x^{2} + 2 x^{4} \cdot 2 x + 2 x^{4} \cdot 2 - 8 x^{2} - 8 \cdot 2 x - 8 \cdot 2 : x^{8} - 16

= x^{8} - 16

55 x^{2} - 61 x y - 6 y^{2}

(6 x + 5 y)^{3}

\frac{1 + 1}{x ^{2}}

(3 x^{- 7} \cdot y^{7} \cdot z^{- 5})^{- 1}

25 x^{4} y^{4} - 91 x^{2} y^{4} - 36 y^{4}

What is expand (x^2-2x+2)(x^2-2)(x^2+2x+2)(x^2+2) ?
The solution to expand (x^2-2x+2)(x^2-2)(x^2+2x+2)(x^2+2) is x^8-16