What is factor 27u^3+8n^6m^9 ?

The solution to factor 27u^3+8n^6m^9 is (3u+2n^2m^3)(9u^2-6n^2m^3u+4n^4m^6)

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factor 27u^3+8n^6m^9

factor

27 u^{3} + 8 n^{6} m^{9}

(3 u + 2 n^{2} m^{3}) (9 u^{2} - 6 n^{2} m^{3} u + 4 n^{4} m^{6})

Solution steps

27 u^{3} + 8 n^{6} m^{9}

Rewrite

27 u^{3}

(3 u)^{3}

Rewrite

8 n^{6} m^{9}

(2 n^{2} m^{3})^{3}

= (3 u)^{3} + (2 n^{2} m^{3})^{3}

Apply Sum of Cubes Formula:

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

(3 u)^{3} + (2 n^{2} m^{3})^{3} = (3 u + 2 n^{2} m^{3}) ((3 u)^{2} - 2 n^{2} m^{3} 3 u + (2 n^{2} m^{3})^{2})

= (2 n^{2} m^{3} + 3 u) ((2 n^{2} m^{3})^{2} - 2 n^{2} m^{3} 3 u + (3 u)^{2})

Simplify

(3 u + 2 n^{2} m^{3}) ((3 u)^{2} - 2 n^{2} m^{3} \cdot 3 u + (2 n^{2} m^{3})^{2}) : (3 u + 2 n^{2} m^{3}) (9 u^{2} - 6 n^{2} m^{3} u + 4 n^{4} m^{6})

= (3 u + 2 n^{2} m^{3}) (9 u^{2} - 6 n^{2} m^{3} u + 4 n^{4} m^{6})

x^{2 - 3 x - 6}

18 - 103

x + (x - 1) + 3 (x - 3)

- b^{6} - 12 b^{2} + 8 + 6 b^{4}

50 x - 2 x

What is factor 27u^3+8n^6m^9 ?
The solution to factor 27u^3+8n^6m^9 is (3u+2n^2m^3)(9u^2-6n^2m^3u+4n^4m^6)