What is factor a^6-1 ?

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

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factor a^6-1

factor

a^{6} - 1

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

Solution steps

a^{6} - 1

Apply exponent rules

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

Apply Difference of Cubes Formula:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

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

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

Factor

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

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

Factor

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

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

x^{2} + 11 x + 42 = 0

9 x > 3

- \frac{2}{3} ab c + \frac{1}{4} ab c - \frac{1}{12} ab c - \frac{7}{8} ab

3 a > - 6 and 2 a + 4 < 6

\frac{1}{2} (\frac{2}{3})^{2} - 4 (\frac{2}{3}) + 6

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