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Understanding Algebraic Identities and Their Applications

This educational resource delves into key algebraic identities, including the expansion and factorization of binomials like (a+b)², (a-b)², and (a+b)(a-b). It explains the significance of these identities in simplifying expressions and solving mathematical problems. Perfect for students and educators, this guide provides step-by-step explanations, examples, and applications of each identity. Enhance your algebra skills with clear illustrations and practical exercises to reinforce learning.

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Understanding Algebraic Identities and Their Applications

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  1. imAwrI srbsmqwvW AiDAwpk: AjY kumwr srkwrI hweI skUl kotVw klW izlw mwnsw klws=7vIN ivSw=ihswb pwT=7vW ividAwrQIAW dy nwm: gurivMdr isMG inrml isMG jsivMdr kOr gurpRIq kOr

  2. mu~FlI jwxkwrI (a+b) Aqy (a-b) do srl sDwrn do pdI hn[ iehnW nMU iek dUjy jW Awpny nwl guxw krn qy hyT ilKy iqMn guxnPl pRwpq hMudy hn [ 1.(a+b) (a+b) jW (a+b)2----(Awpxy nwl guxw) 2.(a-b) (a-b) jW (a-b)2----(Awpxy nwl guxw) 3.(a+b)(a-b)----(iek dUjy nwl guxw) kil`k kro

  3. 1.(a+b) (a+b) jW (a+b)2----(Awpxy nwl guxw) 2.(a-b) (a-b) jW (a-b)2----(Awpxy nwl guxw) 3.(a+b)(a-b)----(iek dUjy nwl guxw) • ieh guxnPl bIj gixq ivc kMm AwauNdy hn[ • iehnW guxnPlW dI shwieqw nwl AsIN swDwrx guxW krn nwloN AswnI nwl guxnPl pRwpq kr skdy hW[ kil`k kro

  4. audwhrn 1 1. (a+b) 2 (a+b) 2 =(a+b)(a+b) =a(a+b) +b(a+b) =a2+ab+ba+b2 =a2+(ab+ab)+b2 =a2+2ab+b2 ies qrHW (a+b)2=a2+2ab+b2 kil`k kro

  5. (a+b)2nUM Awm qOr qy ie`k do pdI vrg jW do pdI dw vrg ikhw jWdw hY[ dUsry SbdW iv`c iksy do pdI dw vrg ausdy pihly pd dy vrg ausdy dUsry pdW dy vrg Aqy ausdy dovyN pdW dy gunxPl dy du`gxy dw joV huMdw hY[ jW (pihlw pd+dUjw pd)2=(pihlw pd)2+(dUjw pd)2+2 guxW (pihlw pd¿dUjw pd) (a+b) 2=a 2+2ab+b 2 jW (a+b) 2=a 2+b 2+2ab kil`k kro

  6. audwhrn 2 (a-b)2=a2+2a(-b)+(-b)2 ies qrW swnUM hyT ilKI srbsmqw pRwpq huMdI hY[ (a-b)2=a2-2ab+b2 jW (a-b)2= a2+b2-2ab kil`k kro

  7. SbdW iv`c ies qrW kih skdy hW ik do pdI AMqr (a-b)2Bwv pihly pd dy vrg iv`c dUsry pd dw vrg joV ky joVPl iv`coN dovyN pdW dy gunxPl dw du~gxw Gtw dyx qy pRwpq huMdw hY[ jW (pihlw pd - dUjw pd)2=(pihlw pd)2+(dUjw pd)2 - 2¿(pihlw pd¿dUjw pd) kil`k kro

  8. audwhrn 3 (a+b)(a-b) (a+b)(a-b) = a(a-b)+b(a-b) = a2-ab+ba-b2 (a+b)(a-b) = a2-b2 do pdI joV (a+b) Aqy do pdI AMqr (a-b) dw gunxPl (a+b)(a-b) pihly pd dy vrg iv`coN dUsry pd dy vrg nUM Gtwaux qoN pRwpq ho jWdw hY[ jW (pihlw pd + dUjw pd)(pihlw pd - dUjw pd)=(pihlw pd)2 - (dUjw pd)2 kil`k kro

  9. AiBAws

  10. hyT ilKy pRSnW nUM h`l kro • loVINdI srbsmqw dw pRXog krky gunxPl pqw kro: • a. (y+2)(y+2) b. (3a+4b)(3a-4b) • 2. loVINdI srbsmqw dw pRXog krky mu~L pqw kro: • a. (a2+b2) (a2-b2) b. (2a+3b)(2a-3b) kil`k kro

  11. sRoq pMjwb skUL is`iKAw borf dI 7vIN dI ihswb dI ikqwb iv`coN http://netanimations.net/_animated_quill_pen_writing_in_book kil`k kro

  12. DMnvwd

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