What is expand (x+1)(x-1)(x^2+x+1)(x^2-x+1) ?

The solution to expand (x+1)(x-1)(x^2+x+1)(x^2-x+1) is x^6-1

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expand (x+1)(x-1)(x^2+x+1)(x^2-x+1)

expand

(x + 1) (x - 1) (x^{2} + x + 1) (x^{2} - x + 1)

x^{6} - 1

Solution steps

(x + 1) (x - 1) (x^{2} + x + 1) (x^{2} - x + 1)

Expand

(x + 1) (x - 1) (x^{2} + x + 1) (x^{2} - x + 1) : (x^{2} - 1) (x^{2} + x + 1) (x^{2} - x + 1)

= (x^{2} - 1) (x^{2} + x + 1) (x^{2} - x + 1)

Expand

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

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

Distribute parentheses

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

Simplify

x^{4} x^{2} + x^{4} (- x) + x^{4} \cdot 1 + x^{3} x^{2} + x^{3} (- x) + x^{3} \cdot 1 - x x^{2} - x (- x) - x \cdot 1 - 1 \cdot x^{2} - 1 \cdot (- x) - 1 \cdot 1 : x^{6} - 1

= x^{6} - 1

x^{- 1} (x)

84 \cdot 2

4 - 15

2 \frac{1}{4} \cdot 3 \frac{2}{7}

What is expand (x+1)(x-1)(x^2+x+1)(x^2-x+1) ?
The solution to expand (x+1)(x-1)(x^2+x+1)(x^2-x+1) is x^6-1