To simplify an expression, collect like terms by adding or subtracting their coefficients: 4x + 2x = 6x, while 4x and 5y stay separate. To multiply terms, multiply the numbers and then the letters, so 4a × 3b = 12ab and 2x × 5x = 10x². When an expression has products and sums, simplify the products first, then collect like terms.
Simplifying rules
- Collect like terms: add or subtract the coefficients
- Multiply terms: numbers × numbers, letters × letters
- a × a = a², a × a² = a³
- Divide terms: divide the numbers, cancel common letters
- The sign in front of a term belongs to that term
Collecting like terms
Like terms have the same letters and powers, so they can be combined by adding or subtracting their coefficients. Unlike terms stay separate. In 4x + 5y + 2x − 3y, collect the x terms to get 6x and the y terms to get 2y, giving 6x + 2y.
The sign in front of each term moves with it. It helps to underline or highlight each set of like terms before combining them.
Multiplying terms
Multiply the numbers together, then the letters. 4a × 3b = 12ab, and 2x × 5x = 10x², because x × x = x². With powers, use the index law: 3x² × 2x = 6x³.
Dividing terms
Write the division as a fraction, divide the numbers and cancel any common letters. 12ab ÷ 3a = 4b, because 12 ÷ 3 = 4 and the a cancels. 10x² ÷ 5x = 2x.
Expressions with products and sums
Follow the order of operations: simplify any products before collecting like terms. In 3 × 2m + 5m, the product 3 × 2m = 6m is done first, then 6m + 5m = 11m.
Simplifying with powers
Terms such as 6x² and −x² are like terms and combine to 5x², but x² and x are not like terms and must stay separate. So 6x² + 2x − x² + 4x simplifies to 5x² + 6x.
Worked examples
Example 1. Simplify 4x + 5y + 2x − 3y.
- x terms: 4x + 2x = 6x.
- y terms: 5y − 3y = 2y.
Answer: 6x + 2y.
Example 2. Simplify 4a × 3b.
- Numbers: 4 × 3 = 12.
- Letters: a × b = ab.
Answer: 12ab.
Example 3. Simplify 3 × 2m + 5m.
- Product first: 3 × 2m = 6m.
- Then collect: 6m + 5m.
Answer: 11m.
Example 4. Simplify 6x² + 2x − x² + 4x.
- x² terms: 6x² − x² = 5x².
- x terms: 2x + 4x = 6x.
Answer: 5x² + 6x.
Example 5. Simplify 12ab ÷ 3a.
- Numbers: 12 ÷ 3 = 4.
- Letters: the a cancels, leaving b.
Answer: 4b.
Example 6. The sides of a triangle are 2x + 1, x + 3 and 3x. Write an expression for the perimeter.
- Add the sides: 2x + 1 + x + 3 + 3x.
- Collect: 6x + 4.
Answer: 6x + 4.
Common mistakes
- Combining unlike terms. 4x + 5y cannot be simplified to 9xy.
- Losing the sign of a term. In 5y − 3y the minus belongs to 3y.
- Adding powers when collecting. 2x² + 3x² = 5x², not 5x⁴.
- Combining x and x². They are not like terms.
- Writing 2x × 5x = 10x. x × x = x², so the answer is 10x².
How simplifying is examined
Simplifying expressions is a Foundation skill in the 1MA1 GCSE and 4MA1 International GCSE, and it is needed in almost every algebra question at Higher tier. Questions ask you to:
- collect like terms in an expression
- multiply or divide terms
- simplify expressions containing powers
- write and simplify an expression for a perimeter or total
The simplifying and expanding worksheet has questions with answers, and the algebra revision engine gives more practice.
This builds on algebraic notation and leads to expanding brackets.
Frequently asked questions
How do you collect like terms?
Group terms with the same letters and powers, then add or subtract their coefficients.
What is 3a × 4a?
12a², because 3 × 4 = 12 and a × a = a².
Can you simplify 2x + 3y?
No. The terms have different letters, so they are not like terms.