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Simplifying algebraic expressions

Tutor: Meera

# Simplifying algebraic expressions

## In a nutshell

Algebra uses a combination of letters and numbers to derive expressions called terms. It helps to find unknown quantities. If there is an unknown quantity, start by giving it a letter name, e.g. $x$. This can then be used in an expression, equation or formula.

## Terms

Terms are a combination of numbers and letters. Algebraic terms which have the same letter are called 'like terms' and can be added or subtracted, e.g. $2x +3x=5x$. This is called simplifying. If terms have different letters, or a different combination of letters, they cannot be added or subtracted, e.g. $2x+3y$ cannot be simplified further.

Note: Take care with negatives. The subtract sign belongs to the term it sits in front of. E.g. In $2x -5y$, the subtract sign belongs to $5y$.

##### Examples

\begin{aligned}2\times x&=2x\\ \ \\8\times t&=8t\\ \ \\-5\times y&=-5y\\ \ \\3\times n\times n&=3n^2\end{aligned}​​

## Expressions

An expression is a string of terms separated by a $+$ or $-$.

##### Examples
 ​$2x+2y$​​ ​$a-2b$​​ ​$x^2-4x+4$​​ ​$xy+x^2+3y+1$​​

## Simplifying expressions

Expressions can be simplified by adding or subtracting various terms. Terms with different powers cannot be added or subtracted.

Note: In order to be combined, two terms should be made of the same letter or same combination of letters.

##### Examples

\begin{aligned}4x+5x&=9x\\ \ \\7y-3y&=4y\\ \ \\p+p+2p&=4p\\ \ \\3x^2+2x&=3x^2+2x\\ \ \\3x^2+2x-x^2-7x&=2x^2-5\\ \ \\4xy+3x-2xy+5y&=2xy+3x+5y\end{aligned}​​

Note: if a term has no number in front of it, it is assumed to be $1$. In the example above, $p$ means $1p$. The number $1$ is usually omitted.

It is possible to simplify expressions to help us 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 $=\underline{5x+2y}$

## FAQs - Frequently Asked Questions

### What are terms in algebra?

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