Binomial expansion — A/L Combined Mathematics

How do I practise Binomial expansion?

1 question with a worked solution

Check before you answer: General Term Identification: Writing the (r + 1)-th general term accurately as T_r+1 = ⁿC_r a^n-r b^r including negative signs from b.

1. In the binomial expansion of (a + b)ⁿ where n is a positive integer, what is the total number of terms in the expanded series?
   1. A) n
   2. B) 2ⁿ
   3. C) n - 1
   4. D) n + 1
   Check my answer

   Correct answer: D) n + 1

   The Binomial Theorem gives (a + b)ⁿ = ∑_r=0ⁿ ⁿC_r a^n-r b^r. Since the summation index r runs through all integer values from 0 up to n inclusive, there are exactly n + 1 terms in the expansion.

   Show worked solution

   Step 1: Write expansion: (a + b)ⁿ = ⁿC₀ aⁿ + ⁿC₁ aⁿ⁻¹ b + ... + ⁿC_n bⁿ. Step 2: Count terms from r = 0 to r = n: Total terms = n + 1. Answer: n + 1.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Binomial expansion fit in the syllabus?

Year 2 · Term 1