# Simplifying algebraic expressions

## In a nutshell

Algebraic terms which have the same letter are called 'like terms'. Like terms can be added or subtracted, e.g. $2x + 3x=5x$. This is called simplifying. If terms have different letters, they cannot be simplified, e.g. $5x+3y$. Take care with $+$ or $-$signs. The $-$ belongs to the term it is in front of.

##### Example

*In the expression *$2x-7t$*, the *$-$* belongs to *$7t$*.*

## Simplifying expressions

Terms with different powers cannot be added or subtracted..

##### Examples

$\begin{aligned} 5a+10b-2a-3b&=3a+7b\\ \ \\3x^2+2x&=3x^2+2x \\ \ \\3x^2+2x-x^2+7x&=2x^2+9x\\ \ \\4xy+3x+xy&=3x+5xy\end{aligned}$

*Note: *$3x^2 +2x$* cannot be simplified.*

It is possible to use expressions to help you solve geometric problems.

##### Example 1

*Write an expression for the perimeter of the following shape.*

*Perimeter* $= \underline{2m+2n}$

##### Example 2

*Write an expression for the perimeter of the following shape. Simplify your answer as much as possible.*

$x+y$ | | $x+y$ |

$3x-y$ |

*Perimeter* $=x+y+x+y+3x-y$

*Perimeter* $=\underline{5x+2y}$