$(m + n)$ $(m^{2} - m n + n^{2})$

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Solution

$\begin{matrix} (m + n) (m^{2} - m n + n^{2}) = m (m^{2} - m n + n^{2}) + n (m^{2} - m n + n^{2}) = m^{3} - m^{2} n + m n^{2} + n m^{2} - m n^{2} + n^{3} = m^{3} + n^{3} + (- m^{2} n + m^{2} n) + (m n^{2} - m n^{2}) = m^{3} + n^{3} \end{matrix}$

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(m^{2} - m n + n^{2})

\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^{2} + {m^{'}}^{2} + 2 m m^{'} cos θ = 1

n^{2} + {n^{'}}^{2} + 2 n n^{'} cos θ = 1

m n + m^{'} n^{'} + (m n^{'} + m^{'} n) = cos θ = θ

m^{2} + n^{2} = {csc}^{2} θ

m^{2} + {m^{'}}^{2} + 2 m m^{'} cos x = 1

n^{2} + {n^{'}}^{2} + 2 n n^{'} cos x = 1

m n + m^{'} n^{'} + (m n^{'} + m^{'} n) cos x = 0

m^{2} + n^{2} = c o {sec}^{2} x

{m^{'}}^{2} + {n^{'}}^{2} = c o {sec}^{2} x

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