What is factor 27m^9n^6-8a^3b^3 ?

The solution to factor 27m^9n^6-8a^3b^3 is (3m^3n^2-2ab)(9m^6n^4+6am^3n^2b+4a^2b^2)

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factor 27m^9n^6-8a^3b^3

factor

27 m^{9} n^{6} - 8 a^{3} b^{3}

(3 m^{3} n^{2} - 2 ab) (9 m^{6} n^{4} + 6 a m^{3} n^{2} b + 4 a^{2} b^{2})

Solution steps

27 m^{9} n^{6} - 8 a^{3} b^{3}

Rewrite

27 m^{9} n^{6}

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

Rewrite

8 a^{3} b^{3}

(2 ab)^{3}

= (3 m^{3} n^{2})^{3} - (2 ab)^{3}

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

= (3 m^{3} n^{2} - 2 ab) (9 m^{6} n^{4} + 6 a m^{3} n^{2} b + 4 a^{2} b^{2})

m^{18} y^{3} - n^{3} z^{18}

2 a c - 2 b d + 4 a d - b c

\frac{- 25 - 5 51}{2}

(tan (x + c))^{2}

(x + y)^{2} + 2 (x + y) + 1

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