What is factor x^6-64 ?

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

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factor x^6-64

factor

x^{6} - 64

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

Solution steps

x^{6} - 64

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Factor

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

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

Factor

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

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

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

9 u^{2} - 48 u + 64

\frac{9}{12} \cdot \frac{8}{11}

2 r^{2} + 26 r + 72

f = 2^{2} - 2 - 2

3 x^{2} - 7 x + 6 < 0

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