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

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

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factor 8m^3-125n^3

factor

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

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

Solution steps

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

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

5 x + 10 y

4 z^{2} - 4 z + 1

[(x^{2} - 5) (x^{2} + 5)]^{2} x^{0}

(lo g_{10} (a^{b}))^{2}

f - 0.5 f

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