Class 8 Maths · Chapter 13
Short answer: Class 8 Maths Chapter 13 'Algebra Play' (Ganita Prakash Part 2) me algebraic expressions ka addition, subtraction, multiplication, factorisation aur basic identities [(x+y)², (x−y)², (x+y)(x−y)] step-by-step solve kiye gaye hain — CBSE marking scheme style working ke saath.
Chapter 13 'Algebra Play' Ganita Prakash Part 2 ka hai — 2026-27 session ke naye do-part Class 8 Maths syllabus me. Ye chapter Number Play (Chapter 5) me shuru hui variable-based soch ko formal algebra me convert karta hai: expressions ko add/subtract/multiply karna, factorise karna, aur basic identities use karna seekhte hain. Algebra Play Class 9-10 ke polynomials aur quadratic equations ki neev hai.
Chapter 13 Summary — 5 Minute Revision
Algebra Play chapter Class 8 Maths ke naye Ganita Prakash Part 2 (2026-27 session, 14-chapter rationalised syllabus) ka hissa hai. Is chapter me students algebraic expressions ko combine karna, multiply karna, factorise karna aur standard identities [(x+y)², (x−y)², (x+y)(x−y) = x²−y²] use karna seekhte hain — jo direct Number Play (Chapter 5) ki variable-based understanding pe build hota hai aur aage Class 9-10 ke Polynomials chapter ki neev banata hai. Regular practice — especially sign errors avoid karna aur identities correctly apply karna — is chapter me mastery ke liye zaroori hai.
In-Text Questions — Solutions
Try This: 5x aur 3x like terms hain ya unlike? Reasoning do.
Like terms hain — dono me variable 'x' same hai aur power bhi same (1) hai. Sirf coefficients (5 aur 3) different hain, jo allowed hai like terms ke liye.Think and Discuss: (a+b)² aur a²+b² same hote hain kya?
Nahi — (a+b)² = a² + 2ab + b², jisme extra 2ab term hai. a=2, b=3 se check: (2+3)² = 25, par 2²+3² = 4+9 = 13. Dono different hain, isliye middle term kabhi bhool mat na karo.Figure it Out: 4(x+2) ko expand karke simplify karo.
4(x+2) = 4·x + 4·2 = 4x + 8
Exercise Questions — Solutions (Q1–Q8)
1(a). Add the algebraic expressions: 3x + 5y − 2 and −x + 2y + 7.
(3x + 5y − 2) + (−x + 2y + 7)
= (3x − x) + (5y + 2y) + (−2 + 7)
= 2x + 7y + 5
Answer: 2x + 7y + 5
1(b). Subtract 4a − 3b + c from 7a + 2b − 5c.
(7a + 2b − 5c) − (4a − 3b + c)
= 7a − 4a + 2b − (−3b) − 5c − c
= 3a + 5b − 6c
Answer: 3a + 5b − 6c
2. Multiply: (x + 4)(x − 3)
(x + 4)(x − 3) = x·x + x·(−3) + 4·x + 4·(−3)
= x² − 3x + 4x − 12
= x² + x − 12
Answer: x² + x − 12 — ye distributive property ka application hai, do binomials pe apply kiya.
3. Factorise: 6xy + 9x
Common factor dono terms me nikaalo — dono me 3x common hai.
6xy + 9x = 3x(2y + 3)
Answer: 3x(2y + 3)
4. Solve for x: 3x + 7 = 2x + 15
3x − 2x = 15 − 7
x = 8
Check: LHS = 3(8)+7 = 31, RHS = 2(8)+15 = 31 ✓
Answer: x = 8
5. If a rectangle ki length (2x + 3) cm aur breadth (x − 1) cm hai, iska area algebraic expression me likho aur simplify karo.
Area = length × breadth
Area = (2x + 3)(x − 1)
= 2x² − 2x + 3x − 3
= 2x² + x − 3
Answer: (2x² + x − 3) cm²
6. Identify like and unlike terms in: 5x², 3xy, −2x², 7y², 4xy
Like terms: 5x² aur −2x² (same variable, same power) ; 3xy aur 4xy (same variables, same power)
Unlike term: 7y² (koi aur y² wala term nahi hai group me)
7. Verify (x + y)² = x² + 2xy + y² for x = 3, y = 2.
LHS: (3 + 2)² = 5² = 25
RHS = 3² + 2(3)(2) + 2² = 9 + 12 + 4 = 25
LHS = RHS ✓ — identity verified.
Important Equations — Ek Nazar Me
| Rule / Identity | Formula |
|---|---|
| Addition of like terms | ax + bx = (a+b)x |
| Distributive property | a(b + c) = ab + ac |
| Multiplication of binomials | (x+a)(x+b) = x² + (a+b)x + ab |
| Square of sum | (x+y)² = x² + 2xy + y² |
| Square of difference | (x−y)² = x² − 2xy + y² |
| Difference of squares | (x+y)(x−y) = x² − y² |
| Common factor | ab + ac = a(b+c) |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- (x+y)² ko x²+y² likh dena — beech ka 2xy term bhool jaana sabse common galti hai.
- Subtraction karte waqt bracket ke andar sign flip na karna — jaise (7a+2b) − (4a−3b) me −(−3b) ko −3b likh dena, jabki ye +3b banta hai.
- Unlike terms ko add/subtract kar dena — jaise 3x aur 3x² ko galti se same maan lena, jabki power different hai isliye ye unlike terms hain.
- Factorisation me common factor poora na nikaalna — 6xy+9x me sirf '3' nikaalna, poora 3x ignore kar dena.
- Distributive property lagate waqt sirf ek term multiply karna — a(b+c) me sirf ab likh dena, ac bhool jaana.
- Equation solve karte waqt dono sides pe same operation na karna — sirf ek side se number move kar dena bina sign badle.
Board-Style Important Questions
- Simplify: (2x+3y) + (5x−2y) − (x+y) — algebraic expressions ka combined addition-subtraction, school assessments me common question type.
- Factorise: 12ab − 18a — common factor nikaalne wala standard exercise-style question.
- Multiply and simplify: (x+5)(x−5) — difference of squares identity apply karne ka direct application.
- Solve for x: 4(x−2) = 2x + 6 — distributive property + linear equation solving combined question.
- Verify the identity (a−b)² = a² − 2ab + b² for a=7, b=4 — numeric verification type question jo conceptual understanding test karta hai.
- Find the area of a square whose side is (x+3) units, using algebraic identity — real-life application of (x+y)² identity.
Aksar Poochhe Jaane Wale Sawaal
Ganita Prakash Class 8 Chapter 13 'Algebra Play' me kya cover hota hai?
Is chapter me algebraic expressions ka addition, subtraction, multiplication, factorisation aur basic algebraic identities [(x+y)², (x−y)², (x+y)(x−y)] cover hote hain. Ye Number Play (Chapter 5) me build hui variable-sense ko formal algebra ki taraf le jaata hai.
Class 8 maths ka new book name 2026-27 session ke liye kya hai?
NCERT ne purani single-book format hata kar do-part 'Ganita Prakash' (Part 1 + Part 2) launch kiya hai — 14 chapters total (Part 1: chapter 1-7, Part 2: chapter 8-14).
Algebra Play chapter pichle 'distributive property' wale chapter se kaise related hai?
Pichla chapter distributive property ka intro deta hai (a(b+c) = ab+ac); Algebra Play us property ko binomials ke multiplication aur factorisation me apply karta hai — dono chapters ek dusre ke upar build hote hain.
Algebra Play me identities yaad karne ka easy tarika kya hai?
(x+y)² = x²+2xy+y² aur (x−y)² = x²−2xy+y² — dono me sirf middle term ka sign badalta hai. (x+y)(x−y) = x²−y² 'difference of squares' ke naam se yaad rakho — bina expand kiye seedha squares ka difference.
Kya Algebra Play exam ke liye important hai?
Haan — algebraic expressions ka simplification aur factorisation Class 9-10 ki poori algebra (polynomials, quadratic equations) ki neev hai, isliye school assessments me regularly test hota hai.
Class 8 maths old book vs Ganita Prakash me kya practical difference student ko dikhega?
Naye Ganita Prakash me activity-based, exploratory approach hai (jaise 'play', 'explore' naming pattern) jabki purani NCERT book zyada direct definition-example-exercise format follow karti thi. Content coverage broadly similar hai lekin presentation zyada conceptual aur discussion-driven hai.
Class 8 Maths — Saare Chapters
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