hey friend can anybody give answer?
why (-) * (-) = (+)
Its impossible to give an explanation that you would accept without knowing what kind of explanation you would accept!
For example, one can show that a(b+ c)= ab+ ac (the "distributive law"). In particular, if we take a=-x, b=y, c= -y, that says -x(y+ (-y))= -x(y)+ (-x)(-y). But y+(-y)= 0 and -x(0)= 0 so that tells us that -x(y)+ (-x)(-y)= 0. Adding x(y) to both sides, -x(-y)= x(y).
Is that acceptable?
Think of -a as a reflection of a through the origin. Reflecting twice gives you back a: -(-a) = a.
satisfied from this link.....
i was cleared after going through this.
I have a simple explanation if u confined to Integers only
first of u need to know why - * + = -
multiplication is seemed to be derived from addition. Like2*3=2+2+2. and 3+4=3+3+3+3..
So when u write (-3)*4= (-3)+ (-3)+ (-3)+ (-3)=- (-12)
hence it is proved that (-)* (+)= (-)
Now come to (-)* (-)= (+)
Let me say u want to solve the question something like this. (-1)/1. you must have done divisions in primary classes where you make make a pie ∏ shape. write denominator part inside and numerator part outside etc,..
when u do such ting with (-1)/1. then u have two choices for quotient 1 or (-1). If u put 1 then using quotient rule. 1*(-1)+0=1 . But it's wrong so -1 is only answer u can think of..
All this is poor explanation since real numbers and complex number are not taken.
these all are based on logics and data.2+(3+5)=2*8=2*3+2*5 after many tries it was found that is applicable everywhere so it's made as property of numbers.
similar about others...
There are several good explanations here:
mathforum is also not bad..
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