An algebraic expression is formed by combining numbers, letters and operations. Simplifying an expression means writing it in the shortest and clearest form without changing its value.

 

 

Forming expressions

Expressions are often formed from worded statements by identifying the variable and the operations involved.

 

For example, the phrase
“five more than twice a number”
can be written as:

$$
2x + 5
$$

 

The phrase
“three less than a number squared”
can be written as:

$$
x^2 - 3
$$

 

When forming expressions, multiplication is written without a symbol. For example, \( 4x \) means \( 4 \times x \).

 

 

Simplifying expressions by collecting like terms

Like terms are terms that have the same variable part. These can be combined by adding or subtracting their coefficients.

 

For example:

$$
3x + 5x = 8x
$$

 

Another example:

$$
7a - 2a + 4
$$

$$
= 5a + 4
$$

 

Terms with different powers or different letters cannot be combined.

For example:

$$
4x + 3x^2
$$

cannot be simplified further because \( x \) and \( x^2 \) are not like terms.

 

 

Simplifying expressions with brackets

Brackets can be removed by multiplying every term inside the bracket.

 

For example:

$$
3(x + 4)
$$

$$
= 3x + 12
$$

 

With subtraction:

$$
5(2x - 3)
$$

$$
= 10x - 15
$$

 

If there is a negative sign in front of the bracket, every term inside changes sign.

$$
-(x - 6)
$$

$$
= -x + 6
$$

 

 

Simplifying expressions with more than one bracket

For example:

$$
2(x + 3) + (x + 2)
$$

$$
= 2x + 6 + x + 2
$$

$$
= 3x + 8
$$

 

The goal of simplification is to remove brackets where possible and combine like terms so the expression is as clear and concise as possible. Simplified expressions are easier to use in further calculations and problem solving.