What this guide covers
This guide focuses on a number multiplying a linear bracket and collecting like terms. It is not a complete Sec 1 course or a guide to quadratic factorisation.
Three decisions before you simplify
Read the operation before moving any symbols.
- Product: in −3(2x − 5), the entire bracket is multiplied by −3.
- Sign: −3 × 2x gives −6x; −3 × (−5) gives +15.
- Like terms: 4x and −6x can combine. An x term and a constant cannot.
Expand a negative bracket
Simplify 6x − 3(2x − 5).
- Distribute −3: −3(2x − 5) = −6x + 15.
- Write the full expression: 6x − 6x + 15.
- Collect the x terms: the result is 15.
Check: At x = 2, the original gives 12 − 3(−1) = 15. Substitution is a useful error check; one matching value is not a proof of equivalence.
Collect after expanding
Simplify 4(2a − 3) − 3(a + 1).
- Expand each bracket: 8a − 12 − 3a − 3.
- Group like terms: (8a − 3a) + (−12 − 3).
- The result is 5a − 15.
Check: At a = 4, both the original expression and 5a − 15 give 5. Notice that the minus sign belongs to every term in the second product.
What changes between questions?
A bracket may sit inside a longer expression, or inside an equation. The expansion rule stays the same. After expanding an expression, collect like terms. In an equation, any later balancing step must preserve both sides.
- Start with a single bracket such as 4(2x − 1).
- Then include a term outside the bracket, such as 5x − 2(x + 3).
- Finally recognise the same expansion inside an equation. Expanding correctly is one step; it does not by itself solve the equation.
Find the first incorrect step
Compare each line with the operation it was meant to perform.
- −2(x − 4) = −2x − 8: the second product should be positive.
- 3(x + 5) = 3x + 5: the multiplier must reach the constant too.
- 2x + 3 = 5x: unlike terms cannot be collected.
- 2x + 3x = 5x²: adding like terms changes the coefficient, not the power.
Try it yourself
Work on paper, then compare the steps. These checks do not establish mastery.
Expand −4(y − 2).
−4y + 8. Both y and −2 are multiplied by −4.
Simplify 7p − 2(p + 6).
7p − 2p − 12 = 5p − 12.
Simplify 3(2b − 1) + 2(b + 4).
6b − 3 + 2b + 8 = 8b + 5.
Where this connects
- Explore the Sec 1 curriculum topics →
Put this focused algebra practice in its wider curriculum context.
- See how algebra connects →
The wider map shows useful mathematical connections; it is not a personalised result or a Sec 1 checklist.
- Later connection: factorisation →
Taking out a common factor reverses expansion. The existing guide also includes more advanced quadratic cases.
Sources and scope
This focused Sec 1 guide is informed by school-paper observations. Bracket and collection tasks recur in Temasek Sec 1 2023 and an unidentified-school Sec 1 G3 2024 timed practice. The level label reflects those observations, not a claim about when every school introduces these skills. Examples here are original. Curriculum guidance is available; a personalised Sec 1 diagnostic is not.