What is factor x^3y^6-z^3 ?

The solution to factor x^3y^6-z^3 is (xy^2-z)(x^2y^4+xy^2z+z^2)

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factor x^3y^6-z^3

factor

x^{3} y^{6} - z^{3}

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

Solution steps

x^{3} y^{6} - z^{3}

Rewrite

x^{3} y^{6}

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

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

8 e^{4} + 2 e^{6}

d [r \frac{d T}{d r}] - r d r

6 - (\frac{16}{1 - e ^{3}})

\frac{3}{4} \cdot 3

4 + (35)

What is factor x^3y^6-z^3 ?
The solution to factor x^3y^6-z^3 is (xy^2-z)(x^2y^4+xy^2z+z^2)