Exam Prep

Factorisation for Math Olympiad: Complete Preparation Guide

Break down expressions and build up your Olympiad algebra skills!

OlympiadClass 8
SparkEd Math18 March 20268 min read
Visual guide to Factorisation for Math Olympiad

Why This Matters

Factorisation is the reverse of expansion, and it is one of the most satisfying mathematical skills to master. In Olympiad papers, factorisation questions test your ability to recognize patterns and break down complex expressions.

For Class 8 students, competition problems go beyond routine factoring. They test whether you can spot common factors in unusual expressions, apply algebraic identities creatively, and use factoring by grouping for complex polynomials.

Best Strategy

Master factorisation:

Step 1: Common Factor Method

Always look for the highest common factor first. 6x2+12x=6x(x+2)6x^2 + 12x = 6x(x + 2).

Step 2: Grouping Method

For four-term expressions, try grouping in pairs: ax+bx+ay+by=x(a+b)+y(a+b)=(a+b)(x+y)ax + bx + ay + by = x(a+b) + y(a+b) = (a+b)(x+y).

Step 3: Identity-Based Factoring

Recognize a2−b2=(a+b)(a−b)a^2 - b^2 = (a+b)(a-b), a2+2ab+b2=(a+b)2a^2 + 2ab + b^2 = (a+b)^2, a2−2ab+b2=(a−b)2a^2 - 2ab + b^2 = (a-b)^2. These identities are your primary factoring tools.

Step 4: Practice on SparkEd

60 curated Olympiad factorisation questions that test pattern recognition.

Practice this topic on SparkEd — free visual solutions and AI coaching

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Common Pitfalls

Mistakes to avoid:

* Missing the common factor — Always factor out the GCF first.
* Identity misrecognition — x2+9x^2 + 9 is NOT (x+3)2(x+3)^2. It is x2+9x^2 + 9 (cannot be factored over reals).
* Sign errors in grouping — Be careful with negative signs when regrouping terms.
* Incomplete factoring — Factor completely. x4−1=(x2+1)(x2−1)=(x2+1)(x+1)(x−1)x^4 - 1 = (x^2+1)(x^2-1) = (x^2+1)(x+1)(x-1).

Practice Questions

Try these!

Question 1

Factorise: x2−10x+25x^2 - 10x + 25

Solution: This is (x−5)2(x-5)^2 using the identity a2−2ab+b2=(a−b)2a^2 - 2ab + b^2 = (a-b)^2.

Question 2

Factorise: 4a2−9b24a^2 - 9b^2

Solution: =(2a)2−(3b)2=(2a+3b)(2a−3b)= (2a)^2 - (3b)^2 = (2a+3b)(2a-3b)

Question 3

Factorise: x3+3x2+3x+1x^3 + 3x^2 + 3x + 1

Solution: This is (x+1)3(x+1)^3 using the cube identity!

How SparkEd Helps

SparkEd offers 60 curated Olympiad-level Factorisation questions for Class 8. Completely free at sparkedmaths.com!

Practice These Topics on SparkEd

Frequently Asked Questions

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