Question

i found that (r-3s+8)+(4r+2s)+(s+8)= 5r+16.... how would you prove or disprove it?

Answer 1

the algebra is the proof!

Answer 2

remove parentheses on left h and side using the distributive law.
then rearrange so that like terms are next to each other using commutative law of addition
then combine like terms using distributive law again.
these laws are the proof

Answer 3

actually now that i look more carefully you can remove the parentheses here just using the associative law of addition, since there is no multiplication to be done.

Answer 4

So, if I wanted to show someone, I would group the like terms...and add?

Answer 5

so proof would look something like this: suppose i wish to "prove" that
\[(2m-n)+(3m+2n)=5m+n\] step 1 by associative law of a addition i can write
\[(2m-n)+(3m+2n)=2m-n+3m+2n\] then by commutative law of addition i can write

\[2m-n+3m+2n=2m+3m+2n-n\] then by distributive law i can write
\[2m+3m+2n-n=(2+3)m+(2-1)n\] and finally plain arithmetic gives me
\[(2+3)m+(2-1)n=5m+n\]

Answer 6

of course in real life you combine like terms with your eyeballs without reference to the basic laws of arithmetic, but they are in play anyway

Answer 7

Good stuff :)

Answer 8

hope it is clear

Answer 9

very.....

Answer 10

thx

Answer 11

Well done,djmajik, you have converted satellite73 into an algebraist:-)

Answer 12

:-)