What is factor x^9+216m^3 ?

The solution to factor x^9+216m^3 is (x^3+6m)(x^6+36m^2-6mx^3)

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factor x^9+216m^3

factor

x^{9} + 216 m^{3}

(x^{3} + 6 m) (x^{6} + 36 m^{2} - 6 m x^{3})

Solution steps

x^{9} + 216 m^{3}

Apply exponent rules

= (x^{3})^{3} + (6 m)^{3}

Apply Sum of Cubes Formula:

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

(x^{3})^{3} + (6 m)^{3} = (x^{3} + 6 m) ((x^{3})^{2} - x^{3} \cdot 6 m + (6 m)^{2})

= (x^{3} + 6 m) ((x^{3})^{2} - x^{3} \cdot 6 m + (6 m)^{2})

Simplify

(x^{3})^{2} - x^{3} \cdot 6 m + (6 m)^{2} : x^{6} - 6 x^{3} m + 36 m^{2}

= (x^{3} + 6 m) (x^{6} - 6 x^{3} m + 36 m^{2})

= (x^{3} + 6 m) (x^{6} + 36 m^{2} - 6 m x^{3})

756

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What is factor x^9+216m^3 ?
The solution to factor x^9+216m^3 is (x^3+6m)(x^6+36m^2-6mx^3)