Year 8 expanding and factorising: the mistakes Victorian students make (and how to fix them)

Expanding brackets and factorising are two of the first algebra skills in the Victorian Curriculum 2.0 where students start losing marks they did not expect to lose. The working looks simple, the steps are short, and yet the same errors show up again and again in Year 8 classrooms across Victoria.

That matters beyond Year 8. These skills sit underneath almost everything in Year 9 and 10 algebra: solving quadratics, simplifying expressions, working with fractions that have pronumerals in them. A shaky foundation here creates a much harder repair job later.

Why this topic catches students off guard

In Year 7, most algebra involves substituting values or collecting like terms. The rules feel manageable. Year 8 introducing expanding and factorising changes the game, because now students need to track both a sign and a multiplication at the same time.

It is not a question of intelligence. It is a question of whether a student has automated the small steps well enough that their attention can sit on the whole problem. Many have not yet, and they rush.

The most common expanding mistakes

Forgetting to multiply the second term

The classic version looks like this: a student sees 3(x + 4) and writes 3x + 4 instead of 3x + 12. They multiply the first term in the bracket and then forget the second.

This happens more in mental arithmetic than on paper. When students are encouraged to write every step, the error drops off quickly.

Getting the sign wrong when expanding with a negative

This one is harder to fix. With something like 2(x - 5), most students manage fine. The trouble arrives with expressions like -3(x - 4). Students will often write -3x - 12 instead of -3x + 12, because multiplying two negatives together feels wrong even when it is right.

The fix is not to tell them the rule again. It is to have them practise enough examples that the pattern becomes automatic.

Stopping halfway through a two-bracket expansion

When students first meet expressions like (x + 3)(x + 2), the FOIL method (or the grid method, depending on their teacher's preference) gives four terms. Many students produce three, dropping either the two middle terms or forgetting to combine them. The final answer should be a trinomial, and if it is not, something has gone missing.

Expanding correctly but then not simplifying

A student correctly expands (x + 5)(x - 1) to get x² + 5x - x - 5, then writes that as the answer without collecting the like terms. The algebra is right; the finish is not.

The most common factorising mistakes

Pulling out only part of the common factor

Asked to factorise 6x + 9, a student might write 3(2x + 9) rather than 3(2x + 3). They found a common factor but not the highest one, and then failed to divide the second term correctly. Checking by expanding the answer is the simplest way to catch this.

Leaving the bracket wrong when checking is skipped

Factorising and then not expanding to verify is a habit that costs marks consistently. At Year 8, this check takes about ten seconds and catches most errors.

Sign errors inside the bracket when factorising a negative

Similar to expanding, factorising when the highest common factor is negative trips students up. Factorising -4x - 12 as -4(x + 3) rather than -4(x + 3) is correct; writing -4(x - 3) is not, but it feels plausible in the moment.

What strong students should do at this stage

For students who are finding the basics comfortable, this is an excellent point to push further. Can they:

• Factorise expressions where the common factor includes a pronumeral, such as 6x² + 10x becoming 2x(3x + 5)?
• Expand and simplify expressions with three or more terms inside a bracket?
• Spot when a factorised form makes an equation easier to solve?

The Victorian Curriculum 2.0 leaves room for extension at Year 8 that connects directly to the Year 9 work on quadratics. Getting comfortable with more complex common factors now makes that transition much smoother.

What to do at home when these errors keep appearing

You do not need to teach algebra to help. A few things that make a real difference:

Ask them to check by expanding. If they have factorised something, they can always verify their answer by multiplying back out. Making this a habit is worth more than any drill.

Slow the written steps down. Most sign errors happen when students do two or three steps in their head at once. Encourage them to write every multiplication separately, at least until it feels automatic.

Practise the specific mistake, not the whole topic. If the issue is negative signs in expansion, there is no need to redo thirty generic bracket questions. Five well-chosen questions on exactly that error, done on separate days, will do more.

Look at which questions went wrong on a test or homework sheet. The pattern is usually there: it is almost always one or two specific error types rather than the whole topic.

A note on Year 9 and why this matters now

Year 9 introduces factorising quadratics. x² + 5x + 6 becoming (x + 2)(x + 3) is a direct extension of everything in Year 8. Students who have not automated the Year 8 skills find Year 9 algebra genuinely difficult, not because Year 9 is unreasonable but because they are trying to learn two things at once.

Fixing expanding and factorising errors in Year 8 is one of the most efficient things a student can do for their future maths results. The investment is small. The payoff runs through Years 9 and 10.

Turn the questions they get wrong into practice

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