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

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

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expand (5m+2n)^3

expand

(5 m + 2 n)^{3}

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

Solution steps

(5 m + 2 n)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

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

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

- 9 x^{- 1}

19 x^{5}

(9 - 9 i) - (- 7 + 2 i)

19 x^{9}

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