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• (a + x)ⁿ = aⁿ + ⁿC₁ a^n-1 x + ⁿC₂ a^n-2x² + ⁿC₃ a^n-3x³ + ... + xⁿ.
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  Applying binomial on (a + b)²

  Using general expansion equation:
  a^2-0 + ₂c¹(a)^2-1(b)¹ + b^2-0 = a²+2ab+ b²

  Applying Binomial on (a + b)³

  a^3-0 + ³c₁a^3-1b¹ + ³c₂ a^3-2b² + b^3-0 = a³ + 3a²b + 3ab² + b³
  And if in this case if particular term say ‘r’ is asked, then instead of applying the whole expansion, the following direct formula can be applied to find the ‘r’th term
• ‘r’th term = x^n–r+1a^{r – 1}[{n(n – 1)(n – 2) ... (n – r + 2)} ÷ (r – 1)!]. Similarly (x + a)ⁿ can be expanded as
• (x + a)ⁿ = xⁿ + ⁿC₁ x^n–1a + ⁿC₁ x^n–2 a² + ⁿC₁ x^n–3 a³ + ... + aⁿ In case of a binomial expansion, if any particular term say ‘r’ is asked, then instead of applying the whole expansion, the following direct formula can be applied to find the ‘r’th term.
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• ‘r’th term = a^n–r+1 x^r–1 [{n(n–1) (n – 2) ... (n – r + 2)} ÷ (r – 1)!] So order of the term to be expanded is very important i.e., whether it is in the form (a + x)ⁿ or (x + a)ⁿ