MYP Maths: Expanding & Factorising FAQ

Expanding means removing brackets by multiplying out an expression, like turning $3(x+2)$ into $3x+6$. Factorising is the reverse: writing an expression as a product of factors, like turning $x^2+5x+6$ into $(x+2)(x+3)$. Both sit under the MYP's Form criterion and appear constantly in equations, graphs and word problems.

Because almost everything after MYP 4-5 depends on it. Solving quadratics, simplifying algebraic fractions, sketching parabolas and even DP-level calculus all assume you can expand and factorise instantly, without thinking about the mechanics. Examiners treat it as a fluency skill, not a topic you revise once and forget.

Expanding starts with brackets and ends with a fully multiplied-out expression; factorising starts with a multiplied-out expression and ends with brackets. They're inverse processes — one always undoes the other, so you can check factorising by expanding your answer back out.

MYP 4-5 covers four main types: common factor (e.g. $6x+9=3(2x+3)$), difference of two squares ($x^2-9=(x-3)(x+3)$), trinomial factorising ($x^2+5x+6=(x+2)(x+3)$), and grouping for four-term expressions. Most exam questions test whether you can spot which type applies before you start.

Practise the distributive law until it's automatic: every term inside the bracket gets multiplied by everything outside it. The most common mistake is forgetting to multiply the second term, or mishandling a negative sign in front of a bracket. Work through double brackets using FOIL (First, Outer, Inner, Last) until you don't need the acronym anymore.

Find two numbers that multiply to give the constant term and add to give the coefficient of $x$. For $x^2+7x+12$, you need two numbers multiplying to 12 and adding to 7 — that's 3 and 4, so it factorises to $(x+3)(x+4)$. Always expand back to check.

The three I mark most often: forgetting to distribute a negative sign across an entire bracket, stopping after finding only one factor pair instead of checking the signs match, and mixing up difference-of-squares with a simple common-factor question. All three are fixed by slowing down on the sign, not by more practice volume.

Most students need 3-4 focused sessions of roughly 30 minutes over two weeks, mixing expanding, factorising and mixed-review questions, rather than one long cram. Fluency here comes from spaced repetition, not from doing fifty identical questions in one sitting.

It's assessed mainly through Criterion A (Knowing and Understanding) in unit tests and end-of-year exams, usually as short-answer questions worth 1-3 marks each, alongside longer problems where factorising is a step towards solving an equation or simplifying a fraction. According to the IB's MYP: Mathematics guide, algebraic manipulation sits within the mandatory content for the Patterns strand across MYP 4-5.

Yes, constantly. Both DP Mathematics: Analysis and Approaches and Mathematics: Applications and Interpretation assume fluent algebraic manipulation from the first week — factorising quadratics to solve equations, expanding brinomials for the binomial theorem, and simplifying rational expressions in calculus. Weak factorising in MYP 4-5 becomes a real handicap in DP 1.

Most students find factorising harder because it requires trial and pattern recognition, while expanding is a mechanical, one-way process. Expanding always works if you follow the distributive law carefully; factorising sometimes has no neat integer solution, which is exactly why the MYP focuses on expressions designed to factorise cleanly.

A mix works best: textbooks explain the method clearly, but most MYP students plateau because they run out of varied practice questions with instant feedback. An online question bank with topical worksheets lets your child drill expanding and factorising specifically, at their own pace, rather than waiting for the next class test to find gaps.

Look for three things: clear worked examples showing each factorising type, a large bank of practice questions with answers, and short topic-specific worksheets rather than whole-textbook chapters. Revision Notes that separate expanding from factorising (rather than blending them) usually help students identify their exact weak spot faster.