What is factor 16x^8-1 ?

The solution to factor 16x^8-1 is (2x^2+2x+1)(2x^2-2x+1)(2x^2+1)(2x^2-1)

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factor 16x^8-1

factor

16 x^{8} - 1

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

Solution steps

16 x^{8} - 1

Apply exponent rules

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

Apply Difference of Two Squares Formula:

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

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

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

Factor

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

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

Factor

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

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

∣ x - 4 ∣ < 3

- \frac{2}{( - \frac{1}{2} + 1 ) ^{2}}

x^{2} - 4 x - 77

∣ x ∣ + 5 \leq 9

(\frac{5}{8})^{- 1}

What is factor 16x^8-1 ?
The solution to factor 16x^8-1 is (2x^2+2x+1)(2x^2-2x+1)(2x^2+1)(2x^2-1)