What is factor m^3n^3-z^6 ?

The solution to factor m^3n^3-z^6 is (mn-z^2)(m^2n^2+mnz^2+z^4)

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factor m^3n^3-z^6

factor

m^{3} n^{3} - z^{6}

(mn - z^{2}) (m^{2} n^{2} + mn z^{2} + z^{4})

Solution steps

m^{3} n^{3} - z^{6}

Rewrite

m^{3} n^{3}

(mn)^{3}

= (mn)^{3} - z^{6}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

z^{6} = (z^{2})^{3}

= (mn)^{3} - (z^{2})^{3}

Apply Difference of Cubes Formula:

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

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

= (mn - z^{2}) (z^{4} + z^{2} mn + (mn)^{2})

Simplify

(mn - z^{2}) ((mn)^{2} + z^{2} mn + z^{4}) : (mn - z^{2}) (m^{2} n^{2} + mn z^{2} + z^{4})

= (mn - z^{2}) (m^{2} n^{2} + mn z^{2} + z^{4})

12 x z - 3 p x - 4 yz + p y

x^{3} + 2 x^{3}

x^{2} y^{2} + ab + a y^{2} + b x^{2}

m^{2} + 2 m^{2} - 10 m - 20

(2 - \infty - \infty) (\infty)

What is factor m^3n^3-z^6 ?
The solution to factor m^3n^3-z^6 is (mn-z^2)(m^2n^2+mnz^2+z^4)