Factorisation is an important mathematics topic for school exams, competitive exams, entrance tests and aptitude preparation. It is useful because many questions can be solved quickly when the definitions, formulas and examples are understood properly.
This tutorial explains factorisation in simple language. It includes meaning, important terms, formulas, step-by-step methods, shortcut ideas, solved examples, practice questions, answers, common mistakes and FAQs.
The best way to learn factorisation is to first understand the rule, then solve easy examples, and then try exam-style questions. This page follows the same order.
What Is Factorisation?
Factorisation is the process of writing an expression as a product of its factors.
Important Terms
| Point | Details |
|---|---|
| Factor | A part that multiplies to form expression |
| Common factor | Factor present in every term |
| Grouping | Arranging terms to take common factors |
| Identity | Standard algebraic formula |
| Quadratic factorisation | Splitting a quadratic expression into two factors |
Important Formulas and Rules
| Point | Details |
|---|---|
| Common factor | ab + ac = a(b+c) |
| Difference of squares | a^2 – b^2 = (a-b)(a+b) |
| Perfect square | a^2 + 2ab + b^2 = (a+b)^2 |
| Perfect square | a^2 – 2ab + b^2 = (a-b)^2 |
| Cubic difference | a^3 – b^3 = (a-b)(a^2+ab+b^2) |
Step-by-Step Method
- Look for common factor first.
- Check if expression matches identity.
- Use grouping if four terms are present.
- For quadratic, split middle term.
- Multiply factors back to check.
Shortcut Ideas
- Always take common factor first.
- Difference of squares needs minus sign.
- Perfect square has middle term 2ab.
- Grouping needs same bracket in both parts.
- Check answer by expansion.
Common Question Types
| Point | Details |
|---|---|
| Common factor | Take factor from all terms |
| Grouping | Pair terms |
| Identity | Use formula |
| Quadratic | Split middle term |
| Cubic | Use cube identities |
Solved Examples
Example 1
Factorise 6x + 9.
Common factor 3. Answer = 3(2x + 3).
Example 2
Factorise x^2 – 9.
(x – 3)(x + 3).
Example 3
Factorise x^2 + 6x + 9.
(x + 3)^2.
Example 4
Factorise x^2 + 5x + 6.
(x + 2)(x + 3).
Example 5
Factorise ab + ac.
a(b + c).
Exam Style Examples
Question 1
Factorise 2x^2 + 8x.
2x(x + 4).
Take highest common factor.
Question 2
Factorise 25 – y^2.
(5 – y)(5 + y).
Difference of squares.
Question 3
Factorise x^2 – 7x + 12.
(x – 3)(x – 4).
Find numbers with product 12 and sum -7.
Common Mistakes
- Not taking common factor first.
- Using difference of squares for addition.
- Wrong signs in quadratic factors.
- Forgetting to check by multiplication.
- Confusing factorisation with expansion.
Practice Questions
- Factorise 4x+8.
- Factorise x^2-16.
- Factorise x^2+4x+4.
- Factorise x^2+7x+10.
- Factorise 3ab+6ac.
- Factorise a^2-b^2.
- Factorise x^2-5x+6.
- Factorise 9-y^2.
- Factorise 2x+2y.
- Factorise x^2+2x+1.
Answers to Practice Questions
- 4(x+2)
- (x-4)(x+4)
- (x+2)^2
- (x+5)(x+2)
- 3a(b+2c)
- (a-b)(a+b)
- (x-2)(x-3)
- (3-y)(3+y)
- 2(x+y)
- (x+1)^2
Frequently Asked Questions
What is factorisation?
Writing an expression as product of factors.
What is common factor?
A factor present in every term.
What is difference of squares?
a squared minus b squared equals (a-b)(a+b).
How to check factorisation?
Multiply factors back.
What is opposite of factorisation?
Expansion.
Revision Notes
In factorisation, always check common factor and identity before using longer methods.
For revision, keep a small formula list and solve a few mixed questions. Do not only read the solution. Try the question first, then compare your steps with the answer.
Conclusion
Factorisation becomes easy when common factors and standard identities are remembered.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Factorisation questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.