Simplification

To reduce something means to make it simpler or write it in a shorter way. In mathematics it means that we collect and rewrite expressions without changing their meaning.

 

Simplification and letters

Simplification is mostly used when working with algebra and equations.

For example:

 

$$ \large 2a+a-3b+b $$

 

Here you must reduce to the simplest form:

We collect all \(a\)

 

$$ \large 2a+a \Leftrightarrow a+a+a \Leftrightarrow 3a $$

 

We collect all \(b\)

 

$$ \large -3b+b \Leftrightarrow -b-b-b+b \Leftrightarrow -2b $$

 

So it can be reduced to:

 

$$ \large 2a-2b $$

 

 

Rules of calculation

When simplifying, all the usual calculation rules and the order of operations apply.

It is very common that there are parentheses in simplification tasks, so you must know the rules for parentheses.