Mnm−nm-nm−n - m2−n2m^2 - n^2m2−n22m+n2m+n2m+n
Expanding the second term using the difference of squares formula a2−b2=(a+b)(a−b)a^2 - b^2 = (a+b)(a-b)a2−b2=(a+b)(a−b):
Mnm−nm-nm−n - (m+n)(m−n)(m+n)(m-n)(m+n)(m−n)2m+n2m+n2m+n
Now, simplify further:
Mnm−nm-nm−n - m+nm+nm+n m−nm-nm−n 2m+n2m+n2m+n
Now, distribute:
Mn^2 - 2m^3n - 2n^3m - n^2m + m^2n
Combine like terms:
Therefore, the final expression is:
Mnm−nm-nm−n - m2−n2m^2 - n^2m2−n22m+n2m+n2m+n
Expanding the second term using the difference of squares formula a2−b2=(a+b)(a−b)a^2 - b^2 = (a+b)(a-b)a2−b2=(a+b)(a−b):
Mnm−nm-nm−n - (m+n)(m−n)(m+n)(m-n)(m+n)(m−n)2m+n2m+n2m+n
Now, simplify further:
Mnm−nm-nm−n - m+nm+nm+n m−nm-nm−n 2m+n2m+n2m+n
Now, distribute:
Mn^2 - 2m^3n - 2n^3m - n^2m + m^2n
Combine like terms:
Mn^2 - 2m^3n - 2n^3m - n^2m + m^2n
Therefore, the final expression is:
Mn^2 - 2m^3n - 2n^3m - n^2m + m^2n