What is factor m^9-n^9 ?

The solution to factor m^9-n^9 is (m-n)(m^2+mn+n^2)(m^6+m^3n^3+n^6)

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factor m^9-n^9

factor

m^{9} - n^{9}

(m - n) (m^{2} + mn + n^{2}) (m^{6} + m^{3} n^{3} + n^{6})

Solution steps

m^{9} - n^{9}

Apply exponent rules

= (m^{3})^{3} - (n^{3})^{3}

Apply Difference of Cubes Formula:

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

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

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

Simplify

(m^{3})^{2} + m^{3} n^{3} + (n^{3})^{2} : m^{6} + m^{3} n^{3} + n^{6}

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

Factor

m^{3} - n^{3} : (m - n) (m^{2} + mn + n^{2})

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

(\frac{4}{9})^{15}

2^{8}

1 - \frac{9}{2}

(8 - 2 i^{4}) + (3 - 7 i^{8}) - (4 + i^{9})

What is factor m^9-n^9 ?
The solution to factor m^9-n^9 is (m-n)(m^2+mn+n^2)(m^6+m^3n^3+n^6)