factorise: m3-n3-m(m2-n2)+n(m-n)3

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Solution

$m^{3} - n^{3} - m (m^{2} - n^{2}) + n (m - n)^{3} (m - n) (m^{2} + m n + n^{2}) - m (m + n) (m - n) + n (m - n)^{3} T a k i n g (m - n) c o m m o n (m - n) [(m^{2} + m n + n^{2}) - m (m + n) + n (m^{2} + n^{2} - 2 m n)] (m - n) [m^{2} + m n + n^{2} - m^{2} - n^{2} + n m^{2} + n^{3} - 2 m n^{2}] (m - n) [m n + n m^{2} + n^{3} - 2 m n^{2}] (m - n) n (m + m^{2} + n^{2} - 2 m n)$

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\frac{m^{3}}{64} + \frac{n^{3}}{27}

\frac{m^{2} - n^{2}}{{(m + n)}^{2}} \times \frac{m^{2} + m n + n^{2}}{m^{3} - n^{3}}

\frac{m^{2} - n^{2}}{{(m + n)}^{2}} \times \frac{m^{2} + m n + n^{2}}{m^{3} - n^{3}}

m \times m \times m \times n \times n \times p \times p \times p \times p

lim n \to \infty [\frac{1}{n^{3}} + \frac{2^{2}}{n^{3}} + \frac{3^{2}}{n^{3}} + \dots + \frac{n^{2}}{n^{3}}]

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