What is factor a^3-m^3n^9 ?

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

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factor a^3-m^3n^9

factor

a^{3} - m^{3} n^{9}

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

Solution steps

a^{3} - m^{3} n^{9}

Rewrite

m^{3} n^{9}

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

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

\frac{3}{5} + \frac{7}{4}

4 x^{2} - 4 x + 1 = 9

x^{2} - 9 y^{2}

\frac{5}{- 3 i}

n^{5}

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