What is factor m^{18}y^3-n^3z^{18} ?

The solution to factor m^{18}y^3-n^3z^{18} is (m^6y-nz^6)(m^{12}y^2+nm^6yz^6+n^2z^{12})

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

factor

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

(m^{6} y - n z^{6}) (m^{12} y^{2} + n m^{6} y z^{6} + n^{2} z^{12})

Solution steps

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

Rewrite

m^{18} y^{3}

(m^{6} y)^{3}

Rewrite

n^{3} z^{18}

(n z^{6})^{3}

= (m^{6} y)^{3} - (n z^{6})^{3}

Apply Difference of Cubes Formula:

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

(m^{6} y)^{3} - (n z^{6})^{3} = (m^{6} y - n z^{6}) ((m^{6} y)^{2} + n z^{6} m^{6} y + (n z^{6})^{2})

= (m^{6} y - n z^{6}) ((n z^{6})^{2} + n z^{6} m^{6} y + (m^{6} y)^{2})

Simplify

(m^{6} y - n z^{6}) ((m^{6} y)^{2} + n z^{6} m^{6} y + (n z^{6})^{2}) : (m^{6} y - n z^{6}) (m^{12} y^{2} + n m^{6} y z^{6} + n^{2} z^{12})

= (m^{6} y - n z^{6}) (m^{12} y^{2} + n m^{6} y z^{6} + n^{2} z^{12})

(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

(sin (2 x))^{4}

What is factor m^{18}y^3-n^3z^{18} ?
The solution to factor m^{18}y^3-n^3z^{18} is (m^6y-nz^6)(m^{12}y^2+nm^6yz^6+n^2z^{12})