What is factor x^8-16 ?

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

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factor x^8-16

factor

x^{8} - 16

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

Solution steps

x^{8} - 16

Apply exponent rules

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

Apply Difference of Two Squares Formula:

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

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

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

Factor

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

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

Factor

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

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

x^{2} + 14 x = 2 x - 32

5 = ∣ 2 z + 3 ∣

\frac{1}{3} + \frac{1}{3}

n^{2} + 4 n - 60

\frac{1}{x} - 4 = 3

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