Algebraic Identities Class 9 Maths Worksheet with Quiz and Activities
Expand squares, multiply with identities, factorise trinomials and build algebra tiles in 2D and 3D. On WitKnowLearn you get the Algebraic Identities Class 9 online quiz, online activities and interactive games, an identity lab, a virtual lab and a worksheet-style practice sheet for NCERT Ganita Manjari Chapter 4.
Algebraic Identities Class 9 Online Quiz
20 questions: 10 easy, 5 average and 5 thinking. Tap an answer and the next question comes up.
Algebraic Identities Class 9 Activities
👆 Tap a tab to switch: Learn, Games, Labs, Challenges, Virtual Lab and Practice sheet
Algebraic Identities: the Story of Identities
A short read for Class 9 before you play. These notes follow Chapter 4 of NCERT Ganita Manjari, Part I.
🟦 Identities from areas
Draw a square of side a + b and cut it into four pieces. The pieces a², ab, ab and b² give (a + b)² = a² + 2ab + b² without any algebra.
🧩 Algebra tiles
An x² tile, x strips and unit squares can be packed into a rectangle. The sides of the rectangle are the factors. Tiles for x² + 8x + 15 make a rectangle of sides x + 3 and x + 5.
✂ Difference of squares
Cut a small square from the corner of a big one and rearrange the rest. You get a rectangle of sides a - b and a + b, so a² - b² = (a - b)(a + b).
🧮 Mental maths
Shridharacharya squared numbers with a² = (a + b)(a - b) + b². Today we use identities to find 105² or 104 × 96 in seconds.
🧊 Cubes
A cube of side a + b splits into 8 blocks, which gives (a + b)³ = a³ + 3a²b + 3ab² + b³.
📐 Rational expressions
Factorising lets us cancel common factors, for example (x² - 9)/(x + 3) = x - 3.
Algebraic Identities Class 9 Activities
Expand, factorise and build with tiles on the Number Train. Earn up to 3 stars in every activity.
This page follows NCERT Class 9 Maths Ganita Manjari, Part I, Chapter 4. Students use identities to expand squares, multiply numbers mentally, factorise trinomials and build algebra tiles in 2D and 3D.
The activities are pitched at Class 9 level. Students sort expressions by identity, pop true identities, match names with expansions, test whether a statement is an identity, and solve case studies on paths, plots and cubes. Explore more Class 9 maths worksheets on WitKnowLearn after this chapter.
Formulas and facts to know
| Identity | Expansion | Example |
|---|---|---|
| (a + b)² | a² + 2ab + b² | 102² = 10404 |
| (a − b)² | a² − 2ab + b² | 98² = 9604 |
| (a + b)(a − b) | a² − b² | 52 × 48 = 2496 |
| (a + b)³ | a³ + 3a²b + 3ab² + b³ | 3³ = 27 |
How to use this page
- Flip the six cards and try the Identity Lab in the Learn tab.
- Play the five games and the five labs to practise each identity.
- Finish the five challenges to collect up to 15 points.
- Build the algebra tiles rectangle in the Virtual Lab and look at it in 2D and 3D.
- Take the 20-question online quiz, with assertion and reason and case study questions, and fill in the practice sheet.
Worked examples
(100 + 5)² = 10000 + 1000 + 25 = 11025.
25 − 2 = 23.
34² − 30² = 1156 − 900 = 256 m².
This Algebraic Identities worksheet for Class 9 maths gives you online activities and interactive games that make identities clear. Every activity has a goal, a hint and a short fact, so students learn while they enjoy.
Complete Guide: NCERT Class 9 Maths Algebraic Identities Chapter 4
This guide is for Class 9 students, parents and teachers. It covers Chapter 4 of NCERT Ganita Manjari, Part I, and shows how to use the quiz, labs and games on this page.
Introduction to Algebraic Identities
The chapter shows how areas and volumes explain identities, and how identities help us expand, factorise and simplify.
What is there in this chapter
- Introduction and visualising identities.
- Factorisation using identities.
- Algebra tiles.
- Factorisation without tiles.
- Finding new identities.
- Simplifying rational expressions.
Learning objectives
- Expand squares and cubes of sums and differences.
- Use a² − b² for fast products.
- Factorise x² + bx + c.
- Prove identities with figures.
- Reason with assertions and case studies.
Learning outcomes
- The student can find 104 × 96 = 9984.
- The student can factorise x² − 7x + 12 as (x − 3)(x − 4).
- The student can state that a³ + b³ + c³ = 3abc when a + b + c = 0.
- The student can solve a path-area case study.
Algebraic Identities Class 9 resources on this page
| Resource | What it gives |
|---|---|
| Online quiz | 20 questions: 10 easy, 5 average and 5 thinking, with assertion and reason and case study questions and a full review |
| Flip cards | 6 picture cards with one-line rules |
| Identity Lab | A hands-on lab with 3 rounds |
| Games | 5 interactive games |
| Labs | 5 activity labs |
| Virtual Lab | 2 experiments and a 2D and 3D algebra tiles builder with aim, procedure, observations and conclusion |
| Challenges | 5 challenges, 15 points in all |
| Practice sheet | A worksheet-style sheet with 16 questions, name and date lines and a live score |
Key facts
| Idea | Rule |
|---|---|
| Square of a sum | a² + 2ab + b² |
| Square of a difference | a² − 2ab + b² |
| Difference of squares | (a − b)(a + b) |
| Trinomial factors | Product c and sum b |
| Three squares | (a + b + c)² has 2ab + 2bc + 2ca |
| Cubes | If a + b + c = 0 then a³ + b³ + c³ = 3abc |
Types of questions you may see
- Expand using an identity.
- Find a square or product mentally.
- Factorise a trinomial.
- Find x² + 1/x² from x + 1/x.
- Assertion and reason questions.
- Case studies on paths, plots, tiles and cubes.
Solved examples
100² − 3² = 9991.
49 − 20 = 29.
The numbers −3 and −4 give (x − 3)(x − 4).
4x² + 12xy + 9y².
27 − 8 = 19 cm³.
50 × 44 + 9 = 2209.
Common mistakes
| Mistake | Correct idea |
|---|---|
| Writing (a + b)² = a² + b². | Add the middle term 2ab. |
| Dropping the sign in (a − b)². | The middle term is −2ab but b² is positive. |
| Factorising x² + 9 as (x + 3)(x − 3). | That product is x² − 9. |
| Forgetting corner squares in a path. | Use outer square minus inner square. |
| Wrong signs when factorising. | Check the product and the sum of the two numbers. |
Algebraic Identities in daily life
Architects find areas of paths and floors, and engineers use cubes and squares in design. Mental maths with identities saves time in exams.
Tips for parents and teachers
- Cut paper squares to show (a + b)² as four pieces.
- Make algebra tiles from card.
- Ask students to find three squares near 100 in their heads.
- Practise one assertion and one case study each week.
Related Class 9 Maths Worksheets
- 🔢Number Systems Class 9 Worksheet
- 🧮Polynomials Class 9 Worksheet
- 📍Coordinate Geometry Class 9 Worksheet
- 📈Linear Equations in Two Variables Class 9
- 📐Introduction to Euclids Geometry Class 9
- 📏Lines and Angles Class 9 Worksheet
- 🔺Triangles Class 9 Worksheet with MCQs
- 🔷Quadrilaterals Class 9 Worksheet
- ⭕Circles Class 9 Worksheet with MCQs
- 🧩Herons Formula Class 9 Worksheet
- 📦Surface Area and Volumes Class 9 Worksheet
- 📊Statistics Class 9 Worksheet
Algebraic Identities Class 9 FAQs
What is Chapter 4 of NCERT Class 9 Maths Ganita Manjari?
Chapter 4 is Exploring Algebraic Identities. It covers visualising identities with areas, factorisation using identities, algebra tiles, factorising without tiles, finding new identities and simplifying rational expressions.
What is an algebraic identity?
An algebraic identity is an equation that is true for every value of its variables. For example (a + b)^2 = a^2 + 2ab + b^2 is true for all numbers a and b.
What are the three standard identities of Class 9?
They are (a + b)^2 = a^2 + 2ab + b^2, (a - b)^2 = a^2 - 2ab + b^2 and a^2 - b^2 = (a - b)(a + b). Together they cover most expansions and factorisations in this chapter.
How do you prove (a + b)^2 = a^2 + 2ab + b^2 with a figure?
Draw a square of side a + b. Cut it into a square of area a^2, two rectangles of area ab each and a square of area b^2. The total area is a^2 + 2ab + b^2.
How do you find 105^2 quickly?
Write 105 = 100 + 5. Then 105^2 = 100^2 + 2 x 100 x 5 + 5^2 = 10000 + 1000 + 25 = 11025.
How do you multiply 104 x 96 using an identity?
Both numbers are 4 away from 100. So 104 x 96 = (100 + 4)(100 - 4) = 100^2 - 4^2 = 10000 - 16 = 9984.
How do you factorise x^2 + 7x + 12?
Find two numbers with product 12 and sum 7. They are 3 and 4, so x^2 + 7x + 12 = (x + 3)(x + 4). Algebra tiles show the same thing as a rectangle with sides x + 3 and x + 4.
What is the identity for (a + b + c)^2?
It is a^2 + b^2 + c^2 + 2ab + 2bc + 2ca. Each square appears once and each pair of letters appears twice.
When is a^3 + b^3 + c^3 equal to 3abc?
It holds when a + b + c = 0. For example if a + b + c = 0 and abc = 12, then a^3 + b^3 + c^3 = 36.
What is the expansion of (a + b)^3?
It is a^3 + 3a^2b + 3ab^2 + b^3. A cube of side a + b is cut into 8 blocks: one a^3, three of a^2b, three of ab^2 and one b^3.
What is the method of Shridharacharya for squaring?
It uses a^2 = (a + b)(a - b) + b^2. To find 47^2, take a = 47 and b = 3 so that 47^2 = 50 x 44 + 9 = 2209.
What can students do on this page?
Students can take a 20-question online quiz with assertion and reason and case study questions, play five games, try five online activities, finish five challenges, run the Identity Lab, do two virtual experiments, build an algebra tiles rectangle in 2D and 3D, and fill in a 16-question practice sheet with a Show answers button.
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