TION.Expand binomial THEOREM,⇒ (x² + 3)⁶.As we know that,Binomial Theorem for positive integral index.⇒ (x + a)ⁿ = ⁿC₀xⁿa⁰ + ⁿC₁xⁿ⁻¹a + ⁿC₂xⁿ⁻²a₂ + ===== + ⁿCₙxaⁿ.Using this formula, we get.⇒ (x² + 3)⁶ = ⁶C₀(x²)⁶(3)⁰ + ⁶C₁(x²)⁵(3)¹ + ⁶C₂(x²)⁴(3)² + ⁶C₃(x²)³(3)³ + ⁶C₄(x²)²(3)⁴ + ⁶C₅(x²)¹(3)⁵ + ⁶C₆(x²)⁰(3)⁶.Using this formula, we get.⇒ ⁶C₀ = 6!/0! (6 - 0)! = 1.⇒ ⁶C₁ = 6!/1! (6 - 1)! = 6!/5! = 6.⇒ ⁶C₂ = 6!/2! (6 - 2)! = 15.⇒ ⁶C₃ = 6!/3! (6 - 3)! = 20.⇒ ⁶C₄ = 6!/4! (6 - 4)! = 15.⇒ ⁶C₅ = 6!/5! (6 - 5)! = 6.⇒ ⁶C₆ = 6!/6! (6 - 6)! = 1.⇒ (x² + 3)⁶ = x¹² + 18x¹⁰ + 135x⁸ + 540x⁶ + 1215x⁴ + 1458x² + 729.                                                                                                                                    MORE INFORMATION.MIDDLE TERM in the expansion of (x + a)ⁿ.(1) = If n is even then middle term = (n/2 + 1)th term.(2) = If n is odd then middle terms are = (n + 1/2)th and (n + 3/2)th term binomial coefficient of middle term is the greatest binomial coefficient.