What is expand (m^4+1/5 n)^3 ?

The solution to expand (m^4+1/5 n)^3 is (125m^{12}+75m^8n+n^3+15m^4n^2)/(125)

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expand (m^4+1/5 n)^3

expand

(m^{4} + \frac{1}{5} n)^{3}

\frac{125 m ^{12} + 75 m ^{8} n + n ^{3} + 15 m ^{4} n ^{2}}{125}

Solution steps

(m^{4} + \frac{1}{5} n)^{3}

Apply Perfect Cube Formula:

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

(m^{4} + \frac{1}{5} n)^{3} = (m^{4})^{3} + 3 (m^{4})^{2} \frac{1}{5} n + 3 m^{4} (\frac{1}{5} n)^{2} + (\frac{1}{5} n)^{3}

= (m^{4})^{3} + 3 (m^{4})^{2} \frac{1}{5} n + 3 m^{4} (\frac{1}{5} n)^{2} + (\frac{1}{5} n)^{3}

Simplify

(m^{4})^{3} + 3 (m^{4})^{2} \frac{1}{5} n + 3 m^{4} (\frac{1}{5} n)^{2} + (\frac{1}{5} n)^{3} : \frac{125 m ^{12} + 75 m ^{8} n + n ^{3} + 15 m ^{4} n ^{2}}{125}

= \frac{125 m ^{12} + 75 m ^{8} n + n ^{3} + 15 m ^{4} n ^{2}}{125}

(2 x + 3 y = 6,) (4 x + 6 y = 12)

(2 x y + z^{2}) (3 cos (t))

(\frac{7}{x ^{3}} + 5 x^{5})^{5}

(x) \cdot (x - 4)

100.53 (t - sin (t))

What is expand (m^4+1/5 n)^3 ?
The solution to expand (m^4+1/5 n)^3 is (125m^{12}+75m^8n+n^3+15m^4n^2)/(125)