What is factor 27m^3+125n^3 ?

The solution to factor 27m^3+125n^3 is (3m+5n)(9m^2-15mn+25n^2)

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factor 27m^3+125n^3

factor

27 m^{3} + 125 n^{3}

(3 m + 5 n) (9 m^{2} - 15 mn + 25 n^{2})

Solution steps

27 m^{3} + 125 n^{3}

Apply exponent rules

= (3 m)^{3} + (5 n)^{3}

Apply Sum of Cubes Formula:

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

(3 m)^{3} + (5 n)^{3} = (3 m + 5 n) ((3 m)^{2} - 3 m \cdot 5 n + (5 n)^{2})

= (3 m + 5 n) ((3 m)^{2} - 3 m \cdot 5 n + (5 n)^{2})

Simplify

(3 m)^{2} - 3 m \cdot 5 n + (5 n)^{2} : 9 m^{2} - 15 mn + 25 n^{2}

= (3 m + 5 n) (9 m^{2} - 15 mn + 25 n^{2})

1 + \frac{4}{9}

(8 x^{2} - 1)^{2}

(1 + x - 4 x^{2}) (1 + 2 x + 3 x^{2}) (1 - 2 x + 4 x^{2})

\frac{x + 4}{x ^{2} - 4} - \frac{x + 1}{x ^{2} - 2 x}

- \frac{4}{7 - 6 i}

What is factor 27m^3+125n^3 ?
The solution to factor 27m^3+125n^3 is (3m+5n)(9m^2-15mn+25n^2)