Math

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Prove that if a,b,c,d,f,s are integers, b|(a+c) then
b|(dc²f-a²sf-a²fd+fc²s).

[Guest]

[tex][ dc^{2 }f - a^{2 }sf - a^{2 }fd +fc^{2 }s ][/tex]=

=[ [tex]( dc^{2 }f + c^{2 }fs ) -( a^{2 }fs + a^{2 }df ) ][/tex]=

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

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

=f(d+s)(c-a)(a+c)

b|(a+c) [tex]\Rightarrow[/tex] b| f(d+s)(c-a)(a+c)