What is expand (2m-5n)^3 ?

The solution to expand (2m-5n)^3 is 8m^3-60m^2n+150mn^2-125n^3

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expand (2m-5n)^3

expand

(2 m - 5 n)^{3}

8 m^{3} - 60 m^{2} n + 150 m n^{2} - 125 n^{3}

Solution steps

(2 m - 5 n)^{3}

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

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

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

Simplify

(2 m)^{3} - 3 (2 m)^{2} \cdot 5 n + 3 \cdot 2 m (5 n)^{2} - (5 n)^{3} : 8 m^{3} - 60 m^{2} n + 150 m n^{2} - 125 n^{3}

= 8 m^{3} - 60 m^{2} n + 150 m n^{2} - 125 n^{3}

(3 x + 8)^{5}

(a + b - c)^{2} + (a - b - c)^{2} - 2 (b - c)

36 j^{2} - 100 k

(3 q + b)^{3}

(- x^{3} y^{2} z) (2 x^{3} y^{4} z)^{3}

What is expand (2m-5n)^3 ?
The solution to expand (2m-5n)^3 is 8m^3-60m^2n+150mn^2-125n^3