What is factor 125x^6-27y^3z^9 ?

The solution to factor 125x^6-27y^3z^9 is (5x^2-3yz^3)(25x^4+15x^2yz^3+9y^2z^6)

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factor 125x^6-27y^3z^9

factor

125 x^{6} - 27 y^{3} z^{9}

(5 x^{2} - 3 y z^{3}) (25 x^{4} + 15 x^{2} y z^{3} + 9 y^{2} z^{6})

Solution steps

125 x^{6} - 27 y^{3} z^{9}

Rewrite

125 x^{6}

(5 x^{2})^{3}

Rewrite

27 y^{3} z^{9}

(3 y z^{3})^{3}

= (5 x^{2})^{3} - (3 y z^{3})^{3}

Apply Difference of Cubes Formula:

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

(5 x^{2})^{3} - (3 y z^{3})^{3} = (5 x^{2} - 3 y z^{3}) ((5 x^{2})^{2} + 5 x^{2} 3 y z^{3} + (3 y z^{3})^{2})

= (5 x^{2} - 3 y z^{3}) ((5 x^{2})^{2} + 5 x^{2} 3 y z^{3} + (3 y z^{3})^{2})

Simplify

(5 x^{2} - 3 y z^{3}) ((5 x^{2})^{2} + 5 x^{2} \cdot 3 y z^{3} + (3 y z^{3})^{2}) : (5 x^{2} - 3 y z^{3}) (25 x^{4} + 15 x^{2} y z^{3} + 9 y^{2} z^{6})

= (5 x^{2} - 3 y z^{3}) (25 x^{4} + 15 x^{2} y z^{3} + 9 y^{2} z^{6})

x \cdot e^{3 t} + y \cdot e^{t}

x^{(3)} + 3 x^{''} + 4 x

[sin (y) - 2 sin (x^{2}) sin (2 y)]

12 x + 24 y + m x + 2 m y

1 - cos^{3} (2 x)

What is factor 125x^6-27y^3z^9 ?
The solution to factor 125x^6-27y^3z^9 is (5x^2-3yz^3)(25x^4+15x^2yz^3+9y^2z^6)