Question

Докажите тождества
2) (m^2-n^2)(m^2+n^2)-m^2(m^2-n^2)-m^2n^2=-n^4

Answer 1

$( m^{2} - n^{2} )(m^{2} + n^{2})- m^{2} (m^{2} - n^{2})- m^{2} n^{2} =- n^{4} \\ (m^{4} - n^{4})-m^{4} + m^{2} n^{2}-m^{2} n^{2} =- n^{4} \\ m^{4} - n^{4}-m^{4}=- n^{4} \\ - n^{4}=- n^{4}$