What is expand (a-1)*(a+1)*(a^2+a+1)*(a^2-a+1) ?

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

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expand (a-1)(a+1)(a^2+a+1)*(a^2-a+1)

expand

(a - 1) \cdot (a + 1) \cdot (a^{2} + a + 1) \cdot (a^{2} - a + 1)

a^{6} - 1

Solution steps

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

Expand

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

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

Expand

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

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

Distribute parentheses

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

Simplify

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

= a^{6} - 1

2130829 k^{1} - 18041807671

3 sin^{2} (a) + 3 cos^{2} (a)

36 p^{2} + 84 p + 49

(x - 1) (\frac{x - 5}{4}) (\frac{x + 1}{4})

6.626 x 1 0^{- 3} 4 \cdot 3 x 1 0^{8}

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