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The process of reducing the algebraic expression or equation to its simplest form. The resulting expression or equation should have no brackets no multiple occurrences of the same term.
The above is a type of dictionary definition of simplification, for the moment lets forget about brackets. What do we mean by multiple occurrences of the same term, what is a term.
Here is a simple equation:
Another pair of terms that are of the same type and can be combined are 5 and 9. Here there are no unknowns so in effect they are still just numbers and can be treated as such but note these two numbers
are on opposite sides of the equal sign (=), because of this we cannot just add the two number terms. We have to first get both number terms on to the same side of the equation, this is in fact quite simple
you just move the term you want to the other side of the equal sign but when you do this the sign of the term is reversed. So we could move the 5 to the right of the equal sign and making it -5 or we could
move the 9 to the left side of the equal sign and make it -9. the resulting equation would be:
The reason why the sign of a term is changed when it is moved to the other side of the equal sign is as follows. An equation is like a pair of scales, everything on the left of the equal sign is in the left pan of the scales and everything on the right side of the equal sign is in the right pan. The pans are in balance, if anything is added or taken from the left pan then the same needs to be added or taken from the right pan. In our equation above if we take 5 from the left pan we must take 5 from the right pan as well, when 5 is taken from the left pan which has a 5 none is left and when we take 5 from the right pan we have 9 - 5 in the right pan. It thus appears as if the 5 has been moved from the left pan to the right pan with the sign changed. Now go back to the above equation before the 5 was moved and take 9 from both the left and right pans, what does the equation look like now?
Getting back to the simplification process, we have simplified the equation so far to:
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