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

The solution to expand (5m^2+2n^5)^3 is 125m^6+150m^4n^5+60m^2n^{10}+8n^{15}

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expand (5m^2+2n^5)^3

expand

(5 m^{2} + 2 n^{5})^{3}

125 m^{6} + 150 m^{4} n^{5} + 60 m^{2} n^{10} + 8 n^{15}

Solution steps

(5 m^{2} + 2 n^{5})^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

(5 m^{2})^{3} + 3 (5 m^{2})^{2} \cdot 2 n^{5} + 3 \cdot 5 m^{2} (2 n^{5})^{2} + (2 n^{5})^{3} : 125 m^{6} + 150 m^{4} n^{5} + 60 m^{2} n^{10} + 8 n^{15}

= 125 m^{6} + 150 m^{4} n^{5} + 60 m^{2} n^{10} + 8 n^{15}

\frac{38}{29} i - \frac{24}{2523} i

\frac{1}{3} - \frac{2}{9}

(9 - 2 i) + (- 2 - 5 i)

x^{6} - 36

\frac{100}{12}

What is expand (5m^2+2n^5)^3 ?
The solution to expand (5m^2+2n^5)^3 is 125m^6+150m^4n^5+60m^2n^{10}+8n^{15}