Question

provw that (-x)y=-(xy)=x(-y) using addition and multiplicative axioms?

Answer 1

(-x)y + xy = y[(-x)+x]=y[0] = 0
-(xy)+xy = 0

so xy is the additive inverse of both -(x)y and -(xy) and since inverses are unique, thus
(-x)y = -(xy)

similarly to show for x(-y)

Answer 2

you good?

Answer 3

are you good with this?

Answer 4

why we starts from this (-x)y + xy ?

Answer 5

so we can utilize the distributive property (factor the y out), leaving (-x) and x which are additive inverses.

then -(xy) and xy are also additive inverses and since inverses are unique we show that (-x)y and -(xy) are equivalent

Answer 6

do you follow?

Answer 7

to prove this we have to show additive inverse , m i right ?

Answer 8

it's a way

Answer 9

thank you