What is factor e^{30}-1 ?

The solution to factor e^{30}-1 is (e+1)(e^4-e^3+e^2-e+1)(e-1)(e^4+e^3+e^2+e+1)(e^{20}+e^{10}+1)

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factor e^{30}-1

factor

e^{30} - 1

(e + 1) (e^{4} - e^{3} + e^{2} - e + 1) (e - 1) (e^{4} + e^{3} + e^{2} + e + 1) (e^{20} + e^{10} + 1)

Solution steps

e^{30} - 1

Rewrite

e^{30} - 1

(e^{10})^{3} - 1^{3}

= (e^{10})^{3} - 1^{3}

Apply Difference of Cubes Formula:

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

(e^{10})^{3} - 1^{3} = (e^{10} - 1) (e^{20} + e^{10} + 1)

= (e^{10} - 1) (e^{20} + e^{10} + 1)

Factor

e^{10} - 1 : (e + 1) (e^{4} - e^{3} + e^{2} - e + 1) (e - 1) (e^{4} + e^{3} + e^{2} + e + 1)

= (e + 1) (e^{4} - e^{3} + e^{2} - e + 1) (e - 1) (e^{4} + e^{3} + e^{2} + e + 1) (e^{20} + e^{10} + 1)

tan^{2} (x) - 5 tan (x) + 6

\frac{d ^{2}}{d x ^{2}} ((y) (e^{x}))

3 x + 2 x z - 21 y - 14 yz

1 - \frac{1}{1 - e ^{3}}

What is factor e^{30}-1 ?
The solution to factor e^{30}-1 is (e+1)(e^4-e^3+e^2-e+1)(e-1)(e^4+e^3+e^2+e+1)(e^{20}+e^{10}+1)