Like terms are terms that have the same variable part raised to the same power. Collecting like terms means combining these terms to simplify an expression.

 

Only the coefficients of like terms are added or subtracted. The variable part stays the same.

 

For example, consider the expression:

$$
3x + 5x
$$

 

Both terms contain \( x \), so they are like terms. Add the coefficients:

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

 

Terms that have different variables or different powers are not like terms and cannot be collected.

 

For example:

$$
4x + 3x^2
$$

This cannot be simplified further because \( x \) and \( x^2 \) are different.

 

 

Collecting like terms with constants

Numbers without variables are called constants. Constants can be collected together.

 

For example:

$$
2x + 7 - 3x + 4
$$

 

Group the like terms:

$$
(2x - 3x) + (7 + 4)
$$

 

Simplify:

$$
-x + 11
$$

 

 

Collecting like terms with more than one variable

Like terms must have exactly the same variable part.

 

For example:

$$
5a + 3b - 2a + 7b
$$

 

Collect the \( a \) terms and the \( b \) terms separately:

$$
(5a - 2a) + (3b + 7b)
$$

$$
= 3a + 10b
$$

 

 

Collecting like terms with brackets

Brackets should be expanded before collecting like terms.

 

For example:

$$
2(x + 3) + 4x
$$

 

Expand the bracket:

$$
2x + 6 + 4x
$$

 

Now collect like terms:

$$
6x + 6
$$

 

Collecting like terms makes expressions shorter, clearer and easier to use in further algebraic work.