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 $$=\underline{5x+2y}$$

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