What is factor 27x^6y^{12}-8z^9 ?

The solution to factor 27x^6y^{12}-8z^9 is (3x^2y^4-2z^3)(9x^4y^8+6x^2y^4z^3+4z^6)

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factor 27x^6y^{12}-8z^9

factor

27 x^{6} y^{12} - 8 z^{9}

(3 x^{2} y^{4} - 2 z^{3}) (9 x^{4} y^{8} + 6 x^{2} y^{4} z^{3} + 4 z^{6})

Solution steps

27 x^{6} y^{12} - 8 z^{9}

Rewrite

27 x^{6} y^{12}

(3 x^{2} y^{4})^{3}

Rewrite

8 z^{9}

(2 z^{3})^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

(3 x^{2} y^{4} - 2 z^{3}) ((3 x^{2} y^{4})^{2} + 3 x^{2} y^{4} \cdot 2 z^{3} + (2 z^{3})^{2}) : (3 x^{2} y^{4} - 2 z^{3}) (9 x^{4} y^{8} + 6 x^{2} y^{4} z^{3} + 4 z^{6})

= (3 x^{2} y^{4} - 2 z^{3}) (9 x^{4} y^{8} + 6 x^{2} y^{4} z^{3} + 4 z^{6})

f^{'} (x) 2 x - 3 x^{2}

x^{2} - 40 + 144

2 tan (x^{2} - y^{2})

4 a x + 4 b x - a y - 15 a - b y - 15 b

- t^{2} - 10 + 9

What is factor 27x^6y^{12}-8z^9 ?
The solution to factor 27x^6y^{12}-8z^9 is (3x^2y^4-2z^3)(9x^4y^8+6x^2y^4z^3+4z^6)