What is factor x^3y^6z^{12}-512 ?

The solution to factor x^3y^6z^{12}-512 is (xy^2z^4-8)(x^2y^4z^8+8xy^2z^4+64)

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factor x^3y^6z^{12}-512

factor

x^{3} y^{6} z^{12} - 512

(x y^{2} z^{4} - 8) (x^{2} y^{4} z^{8} + 8 x y^{2} z^{4} + 64)

Solution steps

x^{3} y^{6} z^{12} - 512

Rewrite

x^{3} y^{6} z^{12}

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

= (x y^{2} z^{4})^{3} - 512

Rewrite

512

8^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Refine

= (x y^{2} z^{4} - 8) ((x y^{2} z^{4})^{2} + 8 x y^{2} z^{4} + 64)

Simplify

(x y^{2} z^{4} - 8) ((x y^{2} z^{4})^{2} + 8 x y^{2} z^{4} + 64) : (x y^{2} z^{4} - 8) (x^{2} y^{4} z^{8} + 8 x y^{2} z^{4} + 64)

= (x y^{2} z^{4} - 8) (x^{2} y^{4} z^{8} + 8 x y^{2} z^{4} + 64)

C (6.3)

3 m y + 7 x + 7 m + 3 x y

(r + 1)^{2} - 7 (r + 1) - 30

(3 x + 5) (3 x + 5)

ab + 1 + ab x + x

What is factor x^3y^6z^{12}-512 ?
The solution to factor x^3y^6z^{12}-512 is (xy^2z^4-8)(x^2y^4z^8+8xy^2z^4+64)