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.

	$m$
$n$

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