# In my last doubt, I asked to give a formal proof, for (-)(+)=(-). I was asked by my maths teacher in school, that how when 2 unlike signs are multiplied, why the result is a negative value. Neha ma'am answered this last time, but it was not at all satisfactory.. I wanted one of the formal proofs like Brijendra Pal sir gave me for (-)(-)=(+)..Experts may prefer to that one, to make the answer satisfactory for (-)(+)=(-)...

$Fromthedistributivelawofmultiplicationwehave\phantom{\rule{0ex}{0ex}}a\times \left(b+c\right)=a\times b+a\times c\phantom{\rule{0ex}{0ex}}whichholdsforallrealnumbers.\phantom{\rule{0ex}{0ex}}Soitwillholdifweputa=1,b=-1andc=1\phantom{\rule{0ex}{0ex}}\Rightarrow 1\times \left(\left(-1\right)+1\right)=1\times \left(-1\right)+1\times 1\phantom{\rule{0ex}{0ex}}\mathrm{sin}ce\left(-1\right)+1=0weget\phantom{\rule{0ex}{0ex}}1\times 0=1\times \left(-1\right)+1\phantom{\rule{0ex}{0ex}}0=1\times \left(-1\right)+1\phantom{\rule{0ex}{0ex}}afterchangingsides\phantom{\rule{0ex}{0ex}}\Rightarrow \overline{)1\times \left(-1\right)=-1}$

Hence proved

Regards,

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