## Expressions In algebra, letters are used to stand for numbers.

The letters are often called variables.

It is necessary to be able to add, subtract, multiply and divide algebraic terms.

### Definitions

 An algebraic term can be made up of coefficient, variables and exponents. Like terms have the same variables and exponents. e.g. { 2a, 4a, -6a } are like terms.a is common to all.   { x, 3a2, 6 } are unlike terms. There is no common term. An algebraic expression is a group of terms. e.g. 4x + 3y is an expression.

An expression involving addition and subtraction can be simplified only if it contains like terms.

The like terms are collected together and then added or subtracted.

 Examples Answers Simplify: 4a + 6a 4a + 6a = 10a -2x − 3x -2x − 3x = -5x 12pq − 6pq + 4pq 12pq − 6pq + 4pq = 10pq 3c + 4d2 + 5c 3c + 4d2 + 5c = 3c + 5c + 4d2 = 8c + 4d2 4x2 + 10x2 4x2 + 10x2 = 14x2

### Multiplying

3xy means "3 multiplied by x multiplied by y ".

In terms of this type the number comes first and the variables are usually placed in alphabetical order.

e.g. 3q × 4p = 12pq

Note that numbers are multiplied first and letters (variables) are placed in alphabetical order.

### Words into Symbols

Many maths problems are written in words and these words often have to be changed into algebraic expressions.

 Words Algebra 3 is added to x x + 3 5 is subtracted from y y − 5 z is multiplied by 4 4z w is divided by 10 w⁄10 The product of x and y xy The difference between a and 5 a − 5 The sum of 7 and w 7 + w p is muliplied by q and 5 is added pq + 5 6 multipied by c is equal to 30 6c = 30