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Important Formulas in Algebra

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a list of Algebraic formulas 

  • a2 – b2 = (a – b)(a + b)
  • (a + b)2 = a2 + 2ab + b2
  • a2 + b2 = (a + b)2 – 2ab
  • (a – b)2 = a2 – 2ab + b2
  • (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
  • (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
  • (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
  • (a – b)3 = a3 – 3a2b + 3ab2 – b= a3 – b3 – 3ab(a – b)
  • a3 – b3 = (a – b)(a2 + ab + b2)
  • a3 + b3 = (a + b)(a2 – ab + b2)
  • (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
  • (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
  • a4 – b4 = (a – b)(a + b)(a2 + b2)
  • a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
  • If n is a natural number an – bn = (a – b)(an-1 + an-2b+…+ bn-2a + bn-1)
  • If n is even (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
  • If n is odd (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +an-3b2…- bn-2a + bn-1)
  • (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….)
  • Laws of Exponents (am)(an) = am+n ; (ab)m = amb; (am)n = amn
  • Roots of Quadratic Equation
  • For a quadratic equation ax2 + bx + c = 0 where a ≠ 0, the roots will be given by the equation as
  • Δ = b2 − 4ac is called the discriminant
  • For real and distinct roots, Δ > 0
  • For real and coincident roots, Δ = 0
  • For non-real roots, Δ < 0
  • If α and β are the two roots of the equation ax2 + bx + c = 0 then, α + β = (-b / a) and α × β = (c / a).
  • If the roots of a quadratic equation are α and β, the equation will be (x − α)(x − β) = 0
  • Factorials
  • n! = (1).(2).(3)…..(n − 1).n
  • n! = n(n − 1)! = n(n − 1)(n − 2)! = ….
  • 0! = 1
  • ( a + b ) n = a n + n a n − 1 b + n ( n − 1 ) 2 ! a n − 2 b 2 + n ( n − 1 ) ( n − 2 ) 3 ! a n − 3 b 3 + … . + b n , w h e r e , n > 1

এই চাকরির জন্য প্রতিষ্ঠান আপনার কাছ থেকে কোন অর্থ চাইলে অথবা কোন ধরনের ভুল বা বিভ্রান্তিকর তথ্য দিলে আমরা দায়ী নয়। চাকরি পাওয়ার জন্য কোন ব্যাক্তি / প্রতিষ্ঠানকে অর্থ প্রদান করতে আমরা কাউকে উৎসাহিত করিনা। কোন প্রকার অর্থ লেনদেনের দায়িত্ব আমরা বহন করবো না।

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