Algebraic expressions ko simplify kaise karein?
Short mein jawab
Algebraic expression simplify karne ke liye brackets hataao, yaad rakhte hue ki bracket se pehle minus ho to andar ka har chinh badal jaata hai, aur distributive property se guna kholo. Phir like terms, yaani ek jaise letter-numbers waale terms, aur number terms jodo: 5c + 3c + 10c = 18c. 18c aur 11d jaise unlike terms alag rehte hain.
Koi sawal atak gaya? Photo lo, Lagnever AI step-by-step samjhayega. 7 din ka trial sirf ₹2. Google Play se app lo
Sankhyaon jaise hi niyam
Arithmetic expressions waale chapter mein humne seekha ki terms ki jagah badli ja sakti hai aur unhe samooh mein joda ja sakta hai, brackets dhyaan se hataaye ja sakte hain, aur distributive property chalti hai: jod ka guna, guna-phalon ka jod hai. Letter-numbers sankhyaon ki jagah aate hain, isliye ye saare niyam algebraic expressions pe bhi chalte hain.
Rectangle ki parimiti simplify karna
l lambaai aur b chaudaai waale rectangle ki parimiti p = l + b + l + b hai. Terms ki jagah badalne se l + l + b + b, aur kyunki l + l = 2l aur b + b = 2b, p = 2l + 2b. Dono expressions alag dikhte hain par barabar hain: l = 3 aur b = 4 pe dono 14 dete hain, aur har l aur b pe ek hi value dete hain. Chhota waala simplified roop kehlaata hai.
Like aur unlike terms
Ek dukaan teen din mein c rupaye waali 5, 3 aur 10 pencils bechti hai, isliye pencils se 5c + 3c + 10c milte hain. Yahan c ko 5 + 3 + 10 baar joda gaya hai, isliye distributive property se kul (5 + 3 + 10) × c = 18c; c = ₹50 pe ye ₹900 hai. d rupaye waale erasers se 4d + 6d + d = 11d milte hain, isliye kul 18c + 11d hai. Ise aur simplify nahi kar sakte, kyunki c aur d alag letter-numbers hain.
Ek jaise letter-numbers waale terms, jaise 5c, 3c aur 10c, ya 12n aur −4n, like terms hain; 18c aur 11d jaise terms unlike terms hain. Like terms judkar ek term bante hain; unlike terms alag rehte hain.
Minus waale brackets
Ek dukaan kursi ₹40 aur mez ₹75 mein kiraye pe deti hai aur lautaane pe ₹6 aur ₹10 waapas karti hai. x kursiyon aur y mezon ka kul kharch (40x + 75y) − (6x + 10y) hai. Minus ka chinh doosre bracket ke andar ke chinh badal deta hai, jisse 40x + 75y − 6x − 10y banta hai, aur like terms jodne se (40 − 6)x + (75 − 10)y = 34x + 65y. Shuruaat ko (40x + 75y) + (−6x − 10y) bhi likh sakte the, kyunki bracket ghataana uske inverse ko jodna hai.
Ek quiz mein sahi jawab ka score p aur galat jawab ki penalty q hai. Charu ke rounds 7p − 3q, 8p − 4q aur 6p − 2q dete hain, jo judkar 21p − 9q banta hai; Krishita ka kul 23p − 7q hai. Antar, 23p − 7q − (21p − 9q), simplify hokar 2p + 2q banta hai, jo positive hai, isliye Krishita ka score zyaada hai. Bracket se pehle ki sankhya har term ko guna karti hai: 4(x + y) − y = 4x + 4y − y = 4x + 3y.
Barabar ya nahi?
Do expressions tabhi barabar hain jab letters ki har value pe ek hi value dein. 5u matlab u ka 5 guna, jabki 5 + u matlab u se 5 zyaada; u = 2 pe ye 10 aur 7 dete hain, isliye barabar nahi. Isi tarah 10y − 3 (y ke 10 gune se 3 kam) aur 10(y − 3) (y se 3 kam ka 10 guna) y = 2 pe 17 aur −10 dete hain.
Aam galtiyan
- 3a + 2b, 5 nahi hai: unlike terms nahi judte.
- 6(p + 2) = 6p + 12: dono terms ko guna karo.
- (4x + 3y) − (3x + 4y) = x − y, x + y nahi: minus dono chinh badalta hai.
- 5 − (2 − 6z) = 3 + 6z.
- 2y + (3y − 6) = 5y − 6: bracket se pehle plus kuch nahi badalta.
- 5(2w + 3x + 4w) = 30w + 15x, like terms 10w aur 20w jodne ke baad.
Ye kyun zaroori hai
Simplified expressions padhne, milaane aur use karne mein aasaan hote hain. Letter-numbers kaise likhte aur unki value kaise nikaalte hain, ye letter-numbers kya hain mein hai, aur simplify karke patterns kaise saabit hote hain, ye algebra se patterns mein. Har sawaal ka jawab Chapter 4 ke NCERT solutions mein hai; poore Chapter 4 ke notes bhi dekho.
Practice karo
-
7p − p + 5q − 2q ka simplest form kya hai?
Jawab dekho
Jawab: (b) 6p + 3q
-
5 − (2 − 6z) ka simplest form kya hai?
Jawab dekho
Jawab: (b) 3 + 6z
-
Kya 5u aur 5 + u barabar expressions hain?
Jawab dekho
Jawab: (b) Nahi: u = 2 pe ve 10 aur 7 hain
-
4(x + y) − y ko simplify karo.
Jawab dekho
Jawab: Distributive property se 4(x + y) = 4x + 4y. Phir 4x + 4y − y = 4x + (4 − 1)y = 4x + 3y.
-
Charu ne quiz ke teen rounds mein 7p − 3q, 8p − 4q aur 6p − 2q score kiye. Kul kitna hai, aur p = 4, q = 1 pe kitna?
Jawab dekho
Jawab: Like terms jodkar: (7 + 8 + 6)p − (3 + 4 + 2)q = 21p − 9q. p = 4 aur q = 1 pe ye 84 − 9 = 75 hai.
Students ke sawal
Like aur unlike terms kya hain?
Like terms mein ek jaise letter-numbers hote hain, jaise 5c, 3c aur 10c, ya 12n aur −4n. Inhe jodkar ek term banta hai: 5c + 3c + 10c = 18c. Unlike terms mein alag letter-numbers hote hain, jaise 18c aur 11d, aur ye jud nahi sakte, isliye 18c + 11d pehle se simplest form mein hai.
Algebraic expression mein brackets kaise hataayein?
Bracket se pehle plus ho to bas bracket hata do: 2 + (x + 3) = x + 5. Minus ho to andar ke har term ka chinh badal do: (40x + 75y) − (6x + 10y) = 40x + 75y − 6x − 10y = 34x + 65y. Koi sankhya bracket ko guna kare to har term ko guna karo: 6(p + 2) = 6p + 12.
Kaise pata karein ki do expressions barabar hain?
Do expressions barabar hain agar unke letter-numbers ki har value pe ek hi value milti ho, jo tab pakka hai jab ek simplify hokar doosra ban jaaye, jaise l + b + l + b aur 2l + 2b. Kuch values aazmaane se jaldi pata chalta hai ki kab barabar nahi: y = 2 pe 10y − 3 aur 10(y − 3) 17 aur −10 dete hain.
Koi sawal atak gaya?
Photo lo, Lagnever AI step-by-step samjhayega. 7 din ka trial sirf ₹2.
Google Play se app lo Browser mein kholo
Parents ke liye: trial ke baad plan har mahine UPI ya card autopay se renew hota hai. App mein kabhi bhi cancel kar sakte hain.