What is factor x^6-729 ?

The solution to factor x^6-729 is (x+3)(x-3)(x^2+3x+9)(x^2-3x+9)

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factor x^6-729

factor

x^{6} - 729

(x + 3) (x - 3) (x^{2} + 3 x + 9) (x^{2} - 3 x + 9)

Solution steps

x^{6} - 729

Apply exponent rules

= (x^{2})^{3} - 9^{3}

Apply Difference of Cubes Formula:

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

(x^{2})^{3} - 9^{3} = (x^{2} - 9) (x^{4} + 9 x^{2} + 9^{2})

= (x^{2} - 9) (x^{4} + 9 x^{2} + 9^{2})

Factor

x^{2} - 9 : (x + 3) (x - 3)

= (x + 3) (x - 3) (x^{4} + 9 x^{2} + 9^{2})

Factor

x^{4} + 9 x^{2} + 9^{2} : (x^{2} + 9 + 3 x) (x^{2} + 9 - 3 x)

= (x + 3) (x - 3) (x^{2} + 9 + 3 x) (x^{2} + 9 - 3 x)

= (x + 3) (x - 3) (x^{2} + 3 x + 9) (x^{2} - 3 x + 9)

\frac{5}{3} - \frac{3}{2}

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

- 16 n - 14 n

12 - (- 4)

\frac{200}{25}

What is factor x^6-729 ?
The solution to factor x^6-729 is (x+3)(x-3)(x^2+3x+9)(x^2-3x+9)