Algebraic Identities Class 8 Maths Worksheet with Quiz and Activities
Work with algebraic identities: expand squares and products, spot perfect squares and build 102² on an area square. On WitKnowLearn you get the Algebraic Identities Class 8 online quiz, online activities and interactive games, a identity lab, a virtual lab and a worksheet-style practice sheet for Class 8 Maths.
Algebraic Identities Class 8 Online Quiz
20 questions: 10 easy, 5 average and 5 thinking. Tap an answer and the next question comes up.
Algebraic Identities Class 8 Activities
👆 Tap a tab to switch: Learn, Games, Labs, Challenges, Virtual Lab and Practice sheet
Algebraic Identities: Squares, Products and Shortcuts
A short read for Class 8 before you play. These notes cover Algebraic Identities.
➕ Square of a sum
The identity (a + b)² = a² + 2ab + b² is true for every value of a and b. Picture a big square of side a + b: it splits into a square a², a square b² and two rectangles of area ab each.
➖ Difference and product
In (a - b)² the middle term is minus 2ab, and the last term b² stays plus. In (a + b)(a - b) the middle terms cancel, leaving the difference of squares a² - b².
⚡ Quick mental maths
Identities make hard sums easy. 102² is (100 + 2)², which is 10000 + 400 + 4 = 10404. 51 × 49 is (50 + 1)(50 - 1) = 2500 - 1 = 2499. Splitting into a round number and a small number is the trick.
Algebraic Identities Class 8 Maths Activities
Follow every step on the Number Train. Earn up to 3 stars in every activity.
This page covers Algebraic Identities for Class 8 maths. It covers the identities for the square of a sum and a difference, the difference of squares, products of binomials and quick mental calculations.
The activities are pitched at Class 8 level. Sort expansions by identity, find perfect squares, work out quick squares and build 102² on an area square in the studio. Explore more Class 8 maths worksheets on WitKnowLearn after this chapter.
Key ideas and facts to know
| Identity | Expands to | Example |
|---|---|---|
| (a + b)² | a² + 2ab + b² | 102² = 10404 |
| (a - b)² | a² - 2ab + b² | 98² = 9604 |
| (a + b)(a - b) | a² - b² | 103 × 97 = 9991 |
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 idea.
- Finish the five challenges to collect up to 15 points.
- Do two virtual experiments and build 102² on an area square in the studio.
- Take the 20-question online quiz, with assertion and reason and case study questions, and fill in the practice sheet.
Worked examples
(100 - 1)² = 10000 - 200 + 1 = 9801.
(a + b)² - 2ab = 100 - 42 = 58.
This Algebraic Identities worksheet for Class 8 science gives you online activities and interactive games that make the chapter clear. Every activity has a goal, a hint and a short fact, so students learn while they enjoy.
Complete Guide: Class 8 Maths Algebraic Identities
This guide is for Class 8 students, parents and teachers. It covers Algebraic Identities for Class 8 maths and shows how to use the quiz, labs and games on this page.
Introduction to Algebraic Identities
Algebraic identities are statements that are true for every value of the variables. This topic shows how to expand with them, spot perfect squares and calculate quickly in your head.
What is there in this chapter
- Square of a sum
- Square of a difference
- Difference of squares
- Product of two binomials
- Quick calculations
Learning objectives
- Recall the standard identities.
- Expand expressions with them.
- Use them for numeric shortcuts.
- Find a² + b² from a + b and ab.
- Reason with assertions and case studies.
Learning outcomes
- I can expand with the standard identities.
- I can square numbers near 100 mentally.
- I can spot a perfect square.
Algebraic Identities Class 8 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 plus a studio that builds 102² on an area square |
| 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 |
|---|---|
| (a + b)² | a² + 2ab + b² |
| (a - b)² | a² - 2ab + b² |
| (a + b)(a - b) | a² - b² |
| Identity | true for all values |
| Perfect square | square of a binomial |
Types of questions you may see
- Expand using an identity
- Assertion and reason on cross terms
- Case study on area of a square garden
- Quick mental calculations
Solved examples
(51 + 49)(51 - 49) = 100 × 2 = 200.
(a + b)² - 4ab = 81 - 72 = 9.
Common mistakes
| Mistake | Correct idea |
|---|---|
| Writing (a + b)² as a² + b² | Include the middle term 2ab |
| Using a plus sign in the middle of (a - b)² | The middle term is minus |
| Forgetting to square the coefficient in (2x + 1)² | Square 2 to get 4 |
Algebraic Identities in daily life
Identities help with areas of squares, quick mental calculations, simplifying algebra and checking answers in exams.
Tips for parents and teachers
- Name the identity before you expand.
- Test with a small number to check.
- Practise one assertion and one case study each week.
Related Class 8 Maths Worksheets
- 🧱Class 8 Maths Worksheet: Algebraic Expressions
- ⚖Class 8 Maths Worksheet: Linear Equations in One Variable
- ✖Class 8 Maths Worksheet: Exponents and Powers
- 🟦Class 8 Maths Worksheet: Squares and Square Roots
- 🧠Class 8 Maths Notes and Mind Maps
- 📚Class 8 Maths Worksheets, page 1
- 📚Class 8 Maths Worksheets, page 2
- 📚Class 8 Maths Worksheets, page 3
Algebraic Identities Class 8 FAQs
What is an algebraic identity?
It is an equation that is true for every value of the variables, such as (a + b)² = a² + 2ab + b².
What is the identity for (a - b)²?
(a - b)² = a² - 2ab + b².
How do I find 102² quickly?
Write it as (100 + 2)² = 10000 + 400 + 4 = 10404.
What is the difference of squares?
a² - b² = (a + b)(a - b), because the cross terms cancel.
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 102² on an area square in the area and table views,, and fill in a 16-question practice sheet with a Show answers button.
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