Module 3: Algebra basics · Topic 13 of 26
Simplifying and expanding
Collecting like terms, expanding brackets and factorising
VIDEO LESSON Watch Mr Boston explain simplifying and expanding
Mr Boston
Simplifying makes expressions shorter and tidier, like tidying a messy bedroom.
Three key skills
- Collect like terms: add terms with the same letter. 3a + 5b + 2a − b = 5a + 4b.
- Expand brackets: multiply everything inside by the number outside. 4(x + 3) = 4x + 12.
- Factorise: the opposite of expanding. Take out the highest common factor. 6x + 9 = 3(2x + 3).
Worked examples
Example 1. Simplify 7x + 3 − 2x + 5.
x terms: 7x − 2x = 5x. Numbers: 3 + 5 = 8. Answer 5x + 8.
Example 2. Expand 5(2y − 1).
5 × 2y = 10y and 5 × −1 = −5. Answer 10y − 5.
Example 3. Expand and simplify 3(x + 2) + 2(x − 4).
3x + 6 + 2x − 8 = 5x − 2.
Example 4. Factorise 12a − 8.
The HCF of 12 and 8 is 4: 4(3a − 2).
Top tips and common mistakes
- Each term keeps the sign in front of it.
- x and x² are not like terms; neither are a and ab.
- Check factorising by expanding your answer.
Tayo
I check my factorising by expanding it again. If I get back to the start, I am right!
Practise
Answer as many as you like. Every question is new, and you get a “correct” tick for each one you get right first time. Use “Show answer” to see a worked solution.
Quiz: earn your stamp
Printable worksheet
Simplifying and expanding worksheet. The questions come first and the answers for grown-ups are on the last page, so you can print just the question pages.
Printing is optional. A4 size.