What is factor 1000x^3y^3-z^3 ?

The solution to factor 1000x^3y^3-z^3 is (10xy-z)(100x^2y^2+10xyz+z^2)

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factor 1000x^3y^3-z^3

factor

1000 x^{3} y^{3} - z^{3}

(10 x y - z) (100 x^{2} y^{2} + 10 x yz + z^{2})

Solution steps

1000 x^{3} y^{3} - z^{3}

Rewrite

1000 x^{3} y^{3}

(10 x y)^{3}

= (10 x y)^{3} - z^{3}

Apply Difference of Cubes Formula:

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

(10 x y)^{3} - z^{3} = (10 x y - z) ((10 x y)^{2} + 10 x yz + z^{2})

= (10 x y - z) ((10 x y)^{2} + z 10 x y + z^{2})

Simplify

(10 x y - z) ((10 x y)^{2} + 10 x yz + z^{2}) : (10 x y - z) (100 x^{2} y^{2} + 10 x yz + z^{2})

= (10 x y - z) (100 x^{2} y^{2} + 10 x yz + z^{2})

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

(x + 2 y)^{3} + 1

x^{3} - 6 x - 5 x + 30

x (2 y)

4 x^{2} a + 3 y + 12 a x + y x

What is factor 1000x^3y^3-z^3 ?
The solution to factor 1000x^3y^3-z^3 is (10xy-z)(100x^2y^2+10xyz+z^2)