Math

[Guest]

Prove that (a²-b²)(c-d)²-(ac-ad-bc+bd)(ac-ad+bc-bd)=0.

[Guest]

[tex](a^{2 } - b^{2 } )(c-d)^{2 } -(ac-ad-bc+bd)(ac-ad+bc-bd)[/tex] =?

=[tex](a^{2 } - b^{2 } )(c-d)^{2 } - [ a(c-d) -b(c-d) ].[ a(c-d) +b(c-d) ][/tex]=

=[tex](a^{2 } - b^{2 })(c-d)^{2 }[/tex] -(c-d)(a-b)(c-d)(a+b)=

=[tex](a^{2 } - b^{2 } )( c-d)^{2 }[/tex] -[tex](a^{2 } - b^{2 } )( c-d)^{2 }[/tex]=

= 0