What is factor m^{24}y^3-n^3z^{24} ?

The solution to factor m^{24}y^3-n^3z^{24} is (m^8y-nz^8)(m^{16}y^2+nm^8yz^8+n^2z^{16})

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factor m^{24}y^3-n^3z^{24}

factor

m^{24} y^{3} - n^{3} z^{24}

(m^{8} y - n z^{8}) (m^{16} y^{2} + n m^{8} y z^{8} + n^{2} z^{16})

Solution steps

m^{24} y^{3} - n^{3} z^{24}

Rewrite

m^{24} y^{3}

(m^{8} y)^{3}

Rewrite

n^{3} z^{24}

(n z^{8})^{3}

= (m^{8} y)^{3} - (n z^{8})^{3}

Apply Difference of Cubes Formula:

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

(m^{8} y)^{3} - (n z^{8})^{3} = (m^{8} y - n z^{8}) ((m^{8} y)^{2} + n z^{8} m^{8} y + (n z^{8})^{2})

= (m^{8} y - n z^{8}) ((n z^{8})^{2} + n z^{8} m^{8} y + (m^{8} y)^{2})

Simplify

(m^{8} y - n z^{8}) ((m^{8} y)^{2} + n z^{8} m^{8} y + (n z^{8})^{2}) : (m^{8} y - n z^{8}) (m^{16} y^{2} + n m^{8} y z^{8} + n^{2} z^{16})

= (m^{8} y - n z^{8}) (m^{16} y^{2} + n m^{8} y z^{8} + n^{2} z^{16})

2 a c + 2 a d - 3 b c - 3 b d

x^{2} + 4 + 4

27 x^{3} - 8 a^{3} b^{6}

(x + 5) - x^{2}

(3 x - y)^{2} - 12 (3 x - y) + 36

What is factor m^{24}y^3-n^3z^{24} ?
The solution to factor m^{24}y^3-n^3z^{24} is (m^8y-nz^8)(m^{16}y^2+nm^8yz^8+n^2z^{16})