What is factor m^{12}y^3-n^3z^{12} ?

The solution to factor m^{12}y^3-n^3z^{12} is (m^4y-nz^4)(m^8y^2+nm^4yz^4+n^2z^8)

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factor m^{12}y^3-n^3z^{12}

factor

m^{12} y^{3} - n^{3} z^{12}

(m^{4} y - n z^{4}) (m^{8} y^{2} + n m^{4} y z^{4} + n^{2} z^{8})

Solution steps

m^{12} y^{3} - n^{3} z^{12}

Rewrite

m^{12} y^{3}

(m^{4} y)^{3}

Rewrite

n^{3} z^{12}

(n z^{4})^{3}

= (m^{4} y)^{3} - (n z^{4})^{3}

Apply Difference of Cubes Formula:

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

(m^{4} y)^{3} - (n z^{4})^{3} = (m^{4} y - n z^{4}) ((m^{4} y)^{2} + n z^{4} m^{4} y + (n z^{4})^{2})

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

Simplify

(m^{4} y - n z^{4}) ((m^{4} y)^{2} + n z^{4} m^{4} y + (n z^{4})^{2}) : (m^{4} y - n z^{4}) (m^{8} y^{2} + n m^{4} y z^{4} + n^{2} z^{8})

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

3 e^{m x} m x + 3 e^{m x} m - e^{m x}

π (20)

4 m - 3 n + 12 m x - 9 n x

(m + n)^{2} - (m + n) + 9

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

What is factor m^{12}y^3-n^3z^{12} ?
The solution to factor m^{12}y^3-n^3z^{12} is (m^4y-nz^4)(m^8y^2+nm^4yz^4+n^2z^8)