If a+b=c, and c-b=a, what does bc = ?

a+b=c


c-b=a





what does





bc (b times c) equal?

If a+b=c, and c-b=a, what does bc = ?
if


a + b = c





then


b = c - a


and


c = a + b





so


bc = (c-a)(a+b)





*********************************


Unfortunately, as many other answers tried to do,


it cannot be simplified past this because C is dependent on both the a and b values





To the people who said that bc = b squared OR c squared,


that is obviously wrong.


proved wrong::





Let a=2, b=10


a + b = c


c=12





bc= 10 x 12 = 120





b squared is 100


c squared is 144





those are INCORRECT.





using my formula,


bc = (c-a)(a+b)


bc = (12-2)(2+10)


bc = 10 x 12


bc = 120








I hope I made sense!!
Reply:bc = b*(a+b)


= ab + b squared


or = b squared (a/b +1)
Reply:wait.... what? is there some kind of property to that?!
Reply:i don't know if that's even possible...have you considered "NO Solution"?
Reply:a + b = c


a = c - b {subtract b from both sides}





This is the same as your second piece of information





Impossible
Reply:bc==c^2-2ac+2a^2-c





given a+b=c


c-b=a


then (a+b)(c-b)=ac this is true, by MPE)





solution...





(a+b)(c-b)= ac


ac-ab+bc-b^2=ac


bc= b^2 +ab





from the first equation we can derive b=c-a





then we substitute





bc=(c-a)^2 - (c-a)(a)


=c^2-2ac+a^2 - c + a^2


=c^2-2ac+2a^2-c
Reply:i know that


a/b divided by c/d = ac/bd








/=fractions
Reply:a+b=c


c-b=a





just using the first equation we can solve this;


a+b=c ... therefore b = c -a


therefore B * C = (a+b)(c-a) = ac +bc -a² -ab





EASY ANS: (a+b)*(c-a) OR -a² -ab +bc +ac





This is interesting because we are saying that:


bc = -a² -ab +bc +ac ... %26lt;-- both side have a bc


which means


0 = -a² -ab +ac


0 = -a(a -b +c) = -a(a +c -b) = -a(a +a) %26lt;-- c-b=a is a given


=%26gt; 0 = -a(2a) = -2a² .


=%26gt; a = 0





which means that:


a+b=c ... is really saying ... 0 +b = c


c-b=a ... is really ... c -b = 0


which means b and c are equal!





Therefore the answers to the question is actually:


b*c = b² = c²








CORRECT ANS: bc = b² = c²