ThichToanHoc-Important Mathematical Formulas


ThichToanHoc-Important Mathematical Formulas

  • (a + b)(a – b) = a2 – b2

  • (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

  • (a ± b)2 = a2 + b2± 2ab

  • (a + b + c + d)2 = a2 + b2 + c2 + d2 + 2(ab + ac + ad + bc + bd + cd)

  • (a ± b)3 = a3 ± b3 ± 3ab(a ± b)

  • (a ± b)(a2 + b2 m ab) = a3 ± b3

  • (a + b + c)(a2 + b2 + c2 -ab – bc – ca) = a3 + b3 + c3 – 3abc =
     

    1/2 (a + b + c)[(a – b)2 + (b – c)2 + (c – a)2]


  • when a + b + c = 0, a3 + b3 + c3 = 3abc

  • (x + a)(x + b) (x + c) = x3 + (a + b + c) x2 + (ab + bc + ac)x + abc

  • (x – a)(x – b) (x – c) = x3 – (a + b + c) x2 + (ab + bc + ac)x – abc

  • a4 + a2b2 + b4 = (a2 + ab + b2)( a2 – ab + b2)

  • a4 + b4 = (a2 – √2ab + b2)( a2 + √2ab + b2)

  • an + bn = (a + b) (a n-1 – a n-2 b +  a n-3 b2 – a n-4 b3 +…….. + b n-1)
  • (valid only if n is odd)

  • an – bn = (a – b) (a n-1 + a n-2 b +  a n-3 b2 + a n-4 b3 +……… + b n-1)
  • {where n ϵ N)

  • (a ± b)2n is always positive while -(a ± b)2n is always negative, for any real values of a and b

  • (a – b)2n = (b – a)2” and (a – b)2n+1 = – (b – a)2n+1

  • if α and β are the roots of equation ax2 + bx + c = 0, roots of cx” + bx + a = 0 are 1/α and 1/β.
    if α and β are the roots of equation ax2 + bx + c = 0, roots of ax2 – bx + c = 0 are -α and -β.

    • n(n + l)(2n + 1) is always divisible by 6.

    • 32n leaves remainder = 1 when divided by 8

    • n3 + (n + 1 )3 + (n + 2 )3 is always divisible by 9

    • 102n + 1 + 1 is always divisible by 11

    • n(n2– 1) is always divisible by 6

    • n2+ n is always even

    • 23n-1 is always divisible by 7

    • 152n-1 +l is always divisible by 16

    • n3 + 2n is always divisible by 3

    • 34n – 4 3n is always divisible by 17

    • n! + 1 is not divisible by any number between 2 and n

    (where n! = n (n – l)(n – 2)(n – 3)…….3.2.1)

      for eg 5! = 5.4.3.2.1 = 120 and similarly 10! = 10.9.8…….2.1= 3628800

  • Product of n consecutive numbers is always divisible by n!.

  • If n is a positive integer and p is a prime, then np – n is divisible by p.

  • |x| = x if x ≥ 0 and |x| = – x if x ≤ 0.
  • among all shapes with the same perimeter a circle has the largest area.

  • if one diagonal of a quadrilateral bisects the other, then it also bisects the quadrilateral.

  • sum of all the angles of a convex quadrilateral = (n – 2)180°

  • number of diagonals in a convex quadrilateral = 0.5n(n – 3)

  • let P, Q are the midpoints of the nonparallel sides BC and AD of a trapezium ABCD.Then,
    ΔAPD = ΔCQB.
  • One thought on “ThichToanHoc-Important Mathematical Formulas

    1. bao anh,mong thay giang lai.em ko hieu gi

      ThichToanHoc-Important Mathematical Formulas
      THÁNG BA 21, 2010
      6 Votes
      ThichToanHoc-Important Mathematical Formulas

      (a + b)(a – b) = a2 – b2

      (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

      (a ± b)2 = a2 + b2± 2ab

      (a + b + c + d)2 = a2 + b2 + c2 + d2 + 2(ab + ac + ad + bc + bd + cd)

      (a ± b)3 = a3 ± b3 ± 3ab(a ± b)

      (a ± b)(a2 + b2 m ab) = a3 ± b3

      (a + b + c)(a2 + b2 + c2 -ab – bc – ca) = a3 + b3 + c3 – 3abc =

      1/2 (a + b + c)[(a – b)2 + (b – c)2 + (c – a)2]

      when a + b + c = 0, a3 + b3 + c3 = 3abc

      (x + a)(x + b) (x + c) = x3 + (a + b + c) x2 + (ab + bc + ac)x + abc

      (x – a)(x – b) (x – c) = x3 – (a + b + c) x2 + (ab + bc + ac)x – abc

      a4 + a2b2 + b4 = (a2 + ab + b2)( a2 – ab + b2)

      a4 + b4 = (a2 – √2ab + b2)( a2 + √2ab + b2)

      an + bn = (a + b) (a n-1 – a n-2 b + a n-3 b2 – a n-4 b3 +…….. + b n-1)
      (valid only if n is odd)

      an – bn = (a – b) (a n-1 + a n-2 b + a n-3 b2 + a n-4 b3 +……… + b n-1)
      {where n ϵ N)

      (a ± b)2n is always positive while -(a ± b)2n is always negative, for any real values of a and b

      (a – b)2n = (b – a)2” and (a – b)2n+1 = – (b – a)2n+1

      if α and β are the roots of equation ax2 + bx + c = 0, roots of cx” + bx + a = 0 are 1/α and 1/β.
      if α and β are the roots of equation ax2 + bx + c = 0, roots of ax2 – bx + c = 0 are -α and -β.

      n(n + l)(2n + 1) is always divisible by 6.

      32n leaves remainder = 1 when divided by 8

      n3 + (n + 1 )3 + (n + 2 )3 is always divisible by 9

      102n + 1 + 1 is always divisible by 11

      n(n2- 1) is always divisible by 6

      n2+ n is always even

      23n-1 is always divisible by 7

      152n-1 +l is always divisible by 16

      n3 + 2n is always divisible by 3

      34n – 4 3n is always divisible by 17

      n! + 1 is not divisible by any number between 2 and n
      (where n! = n (n – l)(n – 2)(n – 3)…….3.2.1)

      for eg 5! = 5.4.3.2.1 = 120 and similarly 10! = 10.9.8…….2.1= 3628800

      Product of n consecutive numbers is always divisible by n!.

      If n is a positive integer and p is a prime, then np – n is divisible by p.

      |x| = x if x ≥ 0 and |x| = – x if x ≤ 0.
      among all shapes with the same perimeter a circle has the largest area.

      if one diagonal of a quadrilateral bisects the other, then it also bisects the quadrilateral.

      sum of all the angles of a convex quadrilateral = (n – 2)180°

      number of diagonals in a convex quadrilateral = 0.5n(n – 3)

      let P, Q are the midpoints of the nonparallel sides BC and AD of a trapezium ABCD.Then,
      ΔAPD = ΔCQB.

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