What is factor 64x^6-1 ?

The solution to factor 64x^6-1 is (2x+1)(2x-1)(4x^2+2x+1)(4x^2-2x+1)

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factor 64x^6-1

factor

64 x^{6} - 1

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

Solution steps

64 x^{6} - 1

Apply exponent rules

= (4 x^{2})^{3} - 1^{3}

Apply Difference of Cubes Formula:

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

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

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

Factor

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

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

Factor

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

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

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

- 2 - 4

\frac{4 ^{3}}{3 ^{2}}

- 4 (x + 5) = 2 (x - 16)

36 x^{2} - 121 y^{2}

\frac{6 ( 7 - z )}{5} = z

What is factor 64x^6-1 ?
The solution to factor 64x^6-1 is (2x+1)(2x-1)(4x^2+2x+1)(4x^2-2x+1)