What is factor 125m^3-8n^3 ?

The solution to factor 125m^3-8n^3 is (5m-2n)(25m^2+10mn+4n^2)

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factor 125m^3-8n^3

factor

125 m^{3} - 8 n^{3}

(5 m - 2 n) (25 m^{2} + 10 mn + 4 n^{2})

Solution steps

125 m^{3} - 8 n^{3}

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

(5 m)^{2} + 5 m \cdot 2 n + (2 n)^{2} : 25 m^{2} + 10 mn + 4 n^{2}

= (5 m - 2 n) (25 m^{2} + 10 mn + 4 n^{2})

\frac{( - 24 x ^{3} + 18 x + 6 )}{( 6 x + 3 )}

a \cdot 2 a

6 \cdot 30

6 \cdot 11

- 77

What is factor 125m^3-8n^3 ?
The solution to factor 125m^3-8n^3 is (5m-2n)(25m^2+10mn+4n^2)