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Siliveru Anil Kumar
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#Educational Updates
#🏆పోటీ పరీక్షల స్పెషల్
#📖ఎడ్యుకేషన్✍
#🎓జాబ్ ప్రిపరేషన్📚
#💼TSPSC/ APPSC ప్రత్యేకం
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![Educational Updates - Algebra Complete Formulas 1. ALGEBRAIC IDENTITIEST २. LINEAR EQUATIONS (0+0)2 = 02 + 20b + b2 . General form: ax +b =0 (0= b)2 = 02 . =b 2qb + b2 Solution:| X= (a + b)(a - b) = 0* - b२ (+ b)3 = 03 + 302b + 30b2 ' 03 4. ARITHMETIC PROGRESSION (AP) (0-0)3 = 03 _ 302b + 30b2 . 03 Generol term: ٥n = ٥ + (n - 1)d 03 + b3 = (q + b)(q2' qb + b2) Sum of first n terms: (a - b)(a२ + ab + b२) 03 _ b3 = ' 2 [20'" +(n - 1)d] Sn (a+b+c)? =02+62+c2+2(ab+bc+ca)l 2(a+4) Also Sn 3.QUADRATIC EQUATIONS Standard form: ax2 + bx +c =0 6. BINOMIAL THEOREM Aac 701102 Quadratic Formula: x = 20 nCox" + "Cixn-'0 + (x+a)"= Discriminant (D): D = b२ 4ac nC2xn-202 . 0n Noture of roots: Generql term: T*1 = nCr xn-r qr Real & distinct 070 F 0=0 Real & equall {ತ ೊ D < 0 > No real roots 8. INDICES & EXPONENTS 0 Sum of roots qm x qn = qm*n d Product of roots | am om-n an (am)" = amn 5. GEOMETRIC PROGRESSION (GP) 0=1 General term: On = @rn-1 Sum 0f first n terms: Sn = g(r" _1),r #1 0-m = r 1 Sum to infinity: $ IrI<1 9. LOGARITHMS logu1 = 0 FACTORIAL & COMBINATIONS logaa =1 n! = n(n 1)(n - 2)* logay loga* loga (xy) Permutqtion: np logo(y) llogay logax - Combination: "C logo loga* TI(n --)! X n logx Chunge of buse: logax Relation: "P nCr * r! log 0 Algebra Complete Formulas 1. ALGEBRAIC IDENTITIEST २. LINEAR EQUATIONS (0+0)2 = 02 + 20b + b2 . General form: ax +b =0 (0= b)2 = 02 . =b 2qb + b2 Solution:| X= (a + b)(a - b) = 0* - b२ (+ b)3 = 03 + 302b + 30b2 ' 03 4. ARITHMETIC PROGRESSION (AP) (0-0)3 = 03 _ 302b + 30b2 . 03 Generol term: ٥n = ٥ + (n - 1)d 03 + b3 = (q + b)(q2' qb + b2) Sum of first n terms: (a - b)(a२ + ab + b२) 03 _ b3 = ' 2 [20'" +(n - 1)d] Sn (a+b+c)? =02+62+c2+2(ab+bc+ca)l 2(a+4) Also Sn 3.QUADRATIC EQUATIONS Standard form: ax2 + bx +c =0 6. BINOMIAL THEOREM Aac 701102 Quadratic Formula: x = 20 nCox" + "Cixn-'0 + (x+a)"= Discriminant (D): D = b२ 4ac nC2xn-202 . 0n Noture of roots: Generql term: T*1 = nCr xn-r qr Real & distinct 070 F 0=0 Real & equall {ತ ೊ D < 0 > No real roots 8. INDICES & EXPONENTS 0 Sum of roots qm x qn = qm*n d Product of roots | am om-n an (am)" = amn 5. GEOMETRIC PROGRESSION (GP) 0=1 General term: On = @rn-1 Sum 0f first n terms: Sn = g(r" _1),r #1 0-m = r 1 Sum to infinity: $ IrI<1 9. LOGARITHMS logu1 = 0 FACTORIAL & COMBINATIONS logaa =1 n! = n(n 1)(n - 2)* logay loga* loga (xy) Permutqtion: np logo(y) llogay logax - Combination: "C logo loga* TI(n --)! X n logx Chunge of buse: logax Relation: "P nCr * r! log 0 - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_728035_37bf0be4_1775936678206_sc.jpg?tenant=sc&referrer=pwa-sharechat-service&f=206_sc.jpg "Educational Updates - Algebra Complete Formulas 1. ALGEBRAIC IDENTITIEST २. LINEAR EQUATIONS (0+0)2 = 02 + 20b + b2 . General form: ax +b =0 (0= b)2 = 02 . =b 2qb + b2 Solution:| X= (a + b)(a - b) = 0* - b२ (+ b)3 = 03 + 302b + 30b2 ' 03 4. ARITHMETIC PROGRESSION (AP) (0-0)3 = 03 _ 302b + 30b2 . 03 Generol term: ٥n = ٥ + (n - 1)d 03 + b3 = (q + b)(q2' qb + b2) Sum of first n terms: (a - b)(a२ + ab + b२) 03 _ b3 = ' 2 [20'\" +(n - 1)d] Sn (a+b+c)? =02+62+c2+2(ab+bc+ca)l 2(a+4) Also Sn 3.QUADRATIC EQUATIONS Standard form: ax2 + bx +c =0 6. BINOMIAL THEOREM Aac 701102 Quadratic Formula: x = 20 nCox\" + \"Cixn-'0 + (x+a)\"= Discriminant (D): D = b२ 4ac nC2xn-202 . 0n Noture of roots: Generql term: T*1 = nCr xn-r qr Real & distinct 070 F 0=0 Real & equall {ತ ೊ D < 0 > No real roots 8. INDICES & EXPONENTS 0 Sum of roots qm x qn = qm*n d Product of roots | am om-n an (am)\" = amn 5. GEOMETRIC PROGRESSION (GP) 0=1 General term: On = @rn-1 Sum 0f first n terms: Sn = g(r\" _1),r #1 0-m = r 1 Sum to infinity: $ IrI<1 9. LOGARITHMS logu1 = 0 FACTORIAL & COMBINATIONS logaa =1 n! = n(n 1)(n - 2)* logay loga* loga (xy) Permutqtion: np logo(y) llogay logax - Combination: \"C logo loga* TI(n --)! X n logx Chunge of buse: logax Relation: \"P nCr * r! log 0 Algebra Complete Formulas 1. ALGEBRAIC IDENTITIEST २. LINEAR EQUATIONS (0+0)2 = 02 + 20b + b2 . General form: ax +b =0 (0= b)2 = 02 . =b 2qb + b2 Solution:| X= (a + b)(a - b) = 0* - b२ (+ b)3 = 03 + 302b + 30b2 ' 03 4. ARITHMETIC PROGRESSION (AP) (0-0)3 = 03 _ 302b + 30b2 . 03 Generol term: ٥n = ٥ + (n - 1)d 03 + b3 = (q + b)(q2' qb + b2) Sum of first n terms: (a - b)(a२ + ab + b२) 03 _ b3 = ' 2 [20'\" +(n - 1)d] Sn (a+b+c)? =02+62+c2+2(ab+bc+ca)l 2(a+4) Also Sn 3.QUADRATIC EQUATIONS Standard form: ax2 + bx +c =0 6. BINOMIAL THEOREM Aac 701102 Quadratic Formula: x = 20 nCox\" + \"Cixn-'0 + (x+a)\"= Discriminant (D): D = b२ 4ac nC2xn-202 . 0n Noture of roots: Generql term: T*1 = nCr xn-r qr Real & distinct 070 F 0=0 Real & equall {ತ ೊ D < 0 > No real roots 8. INDICES & EXPONENTS 0 Sum of roots qm x qn = qm*n d Product of roots | am om-n an (am)\" = amn 5. GEOMETRIC PROGRESSION (GP) 0=1 General term: On = @rn-1 Sum 0f first n terms: Sn = g(r\" _1),r #1 0-m = r 1 Sum to infinity: $ IrI<1 9. LOGARITHMS logu1 = 0 FACTORIAL & COMBINATIONS logaa =1 n! = n(n 1)(n - 2)* logay loga* loga (xy) Permutqtion: np logo(y) llogay logax - Combination: \"C logo loga* TI(n --)! X n logx Chunge of buse: logax Relation: \"P nCr * r! log 0 - ShareChat")