Question 103546
{{{(m - n)*(m + n)-(m - n)2}}}
For the first multplication, use the FOIL (First, Outer, Inner, Last) method:
{{{(m-n)(m+n) = m*m + m*n + (-n)*m + (-n)*(n)}}}
{{{(m-n)(m+n) = m^2 + cross(m*n) - cross(m*n) - n^2}}}
{{{(m-n)(m+n) = m^2 - n^2}}}
Substitute into your original expression,
{{{(m - n)*(m + n)-(m - n)2=m^2-n^2-(m-n)2}}}
{{{(m - n)*(m + n)-(m - n)2=m^2-n^2-2m+2n}}}Distributive Property.

{{{(m - n)*(m + n)-(m - n)2=m^2-2m-(n^2-2n)}}}Group like terms.
{{{(m - n)*(m + n)-(m - n)2=m(m-2)-n(n-2)}}}Distributive Property.