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![maths - Algebra Complete Formulas మ 2. LINEAR EQUATIONS १. ALGEBRAIC IDENTITIES (a + b)२ = a२ + २ab + b२ General form: ax + b = 0 -b (0- 0)2 = 02 _ 20b + b2 Solution:| X = (q + b)(d - b) = 02 _ b2 b)3 03 + 302b + 30b2 + b3 (a + ४. ARITHMETIC PROGRESSION (AP) (0 - bj3 = 03 _ 302b + 30b2 _ b3 General term: dn = a + (n - 1)d b) (02 _ 43 + b3 = (q + ab + b२) Sum of first n terms: ( -b) (02 _ a3 _ b3 = + ab + b२) 2 [2q + (n - 1)d] Sn a२ + b२ + c२ + २(ab + bc + ca ) a +b + c)2 = 2 (a+ 4) Also, Sn 3. QUADRATIC EQUATIONS Standard form: ax2 + bx + C = 0 BINOMIAL THEOREM 6 4ac =b + 1b2 _ Quadratic Formula: x 20 nCaxn 1a + nCoxn (x + এ)" = Discriminant (D): D = b2 40c nCzxn-242 . an *+ Nature of roots: Generdl term: Tr+1 = nCr xn-r dr D > 0 _ Reql & distinct D = ০ -> Real & equal D < 0 - No real roots 8. INDICES & EXPONENTS 0 Sum of roots = qm x qn = am+n Product of roots am-n (m)n = 5. GEOMETRIC PROGRESSION (GP) amn General term: dn = arn-1 00 Sum of first n terms: Sn = q(rn- 1),r#1 [ =1 Sum to infinity: $ = Ir| <1 9. LOGARITHMS loga1 = 0 FACTORIAL & COMBINATIONS loga9 a = n! = n(n - 2) loga (xy) | logax logay Permutation: np loga(y) logax - logay Combindtion : nCr logaxn logax n rl(n logx Change of base: logqX ' Relqtion: nP nCr X r! loga Algebra Complete Formulas మ 2. LINEAR EQUATIONS १. ALGEBRAIC IDENTITIES (a + b)२ = a२ + २ab + b२ General form: ax + b = 0 -b (0- 0)2 = 02 _ 20b + b2 Solution:| X = (q + b)(d - b) = 02 _ b2 b)3 03 + 302b + 30b2 + b3 (a + ४. ARITHMETIC PROGRESSION (AP) (0 - bj3 = 03 _ 302b + 30b2 _ b3 General term: dn = a + (n - 1)d b) (02 _ 43 + b3 = (q + ab + b२) Sum of first n terms: ( -b) (02 _ a3 _ b3 = + ab + b२) 2 [2q + (n - 1)d] Sn a२ + b२ + c२ + २(ab + bc + ca ) a +b + c)2 = 2 (a+ 4) Also, Sn 3. QUADRATIC EQUATIONS Standard form: ax2 + bx + C = 0 BINOMIAL THEOREM 6 4ac =b + 1b2 _ Quadratic Formula: x 20 nCaxn 1a + nCoxn (x + এ)" = Discriminant (D): D = b2 40c nCzxn-242 . an *+ Nature of roots: Generdl term: Tr+1 = nCr xn-r dr D > 0 _ Reql & distinct D = ০ -> Real & equal D < 0 - No real roots 8. INDICES & EXPONENTS 0 Sum of roots = qm x qn = am+n Product of roots am-n (m)n = 5. GEOMETRIC PROGRESSION (GP) amn General term: dn = arn-1 00 Sum of first n terms: Sn = q(rn- 1),r#1 [ =1 Sum to infinity: $ = Ir| <1 9. LOGARITHMS loga1 = 0 FACTORIAL & COMBINATIONS loga9 a = n! = n(n - 2) loga (xy) | logax logay Permutation: np loga(y) logax - logay Combindtion : nCr logaxn logax n rl(n logx Change of base: logqX ' Relqtion: nP nCr X r! loga - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_167819_1a50e6cc_1770884165802_sc.jpg?tenant=sc&referrer=pwa-sharechat-service&f=802_sc.jpg "maths - Algebra Complete Formulas మ 2. LINEAR EQUATIONS १. ALGEBRAIC IDENTITIES (a + b)२ = a२ + २ab + b२ General form: ax + b = 0 -b (0- 0)2 = 02 _ 20b + b2 Solution:| X = (q + b)(d - b) = 02 _ b2 b)3 03 + 302b + 30b2 + b3 (a + ४. ARITHMETIC PROGRESSION (AP) (0 - bj3 = 03 _ 302b + 30b2 _ b3 General term: dn = a + (n - 1)d b) (02 _ 43 + b3 = (q + ab + b२) Sum of first n terms: ( -b) (02 _ a3 _ b3 = + ab + b२) 2 [2q + (n - 1)d] Sn a२ + b२ + c२ + २(ab + bc + ca ) a +b + c)2 = 2 (a+ 4) Also, Sn 3. QUADRATIC EQUATIONS Standard form: ax2 + bx + C = 0 BINOMIAL THEOREM 6 4ac =b + 1b2 _ Quadratic Formula: x 20 nCaxn 1a + nCoxn (x + এ)\" = Discriminant (D): D = b2 40c nCzxn-242 . an *+ Nature of roots: Generdl term: Tr+1 = nCr xn-r dr D > 0 _ Reql & distinct D = ০ -> Real & equal D < 0 - No real roots 8. INDICES & EXPONENTS 0 Sum of roots = qm x qn = am+n Product of roots am-n (m)n = 5. GEOMETRIC PROGRESSION (GP) amn General term: dn = arn-1 00 Sum of first n terms: Sn = q(rn- 1),r#1 [ =1 Sum to infinity: $ = Ir| <1 9. LOGARITHMS loga1 = 0 FACTORIAL & COMBINATIONS loga9 a = n! = n(n - 2) loga (xy) | logax logay Permutation: np loga(y) logax - logay Combindtion : nCr logaxn logax n rl(n logx Change of base: logqX ' Relqtion: nP nCr X r! loga Algebra Complete Formulas మ 2. LINEAR EQUATIONS १. ALGEBRAIC IDENTITIES (a + b)२ = a२ + २ab + b२ General form: ax + b = 0 -b (0- 0)2 = 02 _ 20b + b2 Solution:| X = (q + b)(d - b) = 02 _ b2 b)3 03 + 302b + 30b2 + b3 (a + ४. ARITHMETIC PROGRESSION (AP) (0 - bj3 = 03 _ 302b + 30b2 _ b3 General term: dn = a + (n - 1)d b) (02 _ 43 + b3 = (q + ab + b२) Sum of first n terms: ( -b) (02 _ a3 _ b3 = + ab + b२) 2 [2q + (n - 1)d] Sn a२ + b२ + c२ + २(ab + bc + ca ) a +b + c)2 = 2 (a+ 4) Also, Sn 3. QUADRATIC EQUATIONS Standard form: ax2 + bx + C = 0 BINOMIAL THEOREM 6 4ac =b + 1b2 _ Quadratic Formula: x 20 nCaxn 1a + nCoxn (x + এ)\" = Discriminant (D): D = b2 40c nCzxn-242 . an *+ Nature of roots: Generdl term: Tr+1 = nCr xn-r dr D > 0 _ Reql & distinct D = ০ -> Real & equal D < 0 - No real roots 8. INDICES & EXPONENTS 0 Sum of roots = qm x qn = am+n Product of roots am-n (m)n = 5. GEOMETRIC PROGRESSION (GP) amn General term: dn = arn-1 00 Sum of first n terms: Sn = q(rn- 1),r#1 [ =1 Sum to infinity: $ = Ir| <1 9. LOGARITHMS loga1 = 0 FACTORIAL & COMBINATIONS loga9 a = n! = n(n - 2) loga (xy) | logax logay Permutation: np loga(y) logax - logay Combindtion : nCr logaxn logax n rl(n logx Change of base: logqX ' Relqtion: nP nCr X r! loga - ShareChat")