The binomial expansion
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 2 worked examples, 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Expanding without multiplying
- The theorem
Read the transcript of the teaching part
Last time
Before we start: last time, in Arithmetic and geometric progressions, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Expanding without multiplying
Try multiplying out x plus two, to the power ten, by hand. You would multiply ten brackets together. The binomial theorem writes down the answer, term by term, using numbers from Pascal's triangle and the choose function.
The theorem
The expansion of a plus b to the n is a sum of terms, each with a coefficient, a power of a falling, and a power of b rising. The coefficients are the combinations: n C zero, n C one, up to n C n. They form Pascal's triangle. For n equals five: one, five, ten, ten, five, one.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: The binomial expansion · The general term and particular terms.
The whole chapter: Series.
Chapter 12: Series
- Arithmetic and geometric progressions 5 min
- The binomial expansion 5 min
Also for O Level Additional Maths 4037
Which topics come up most in O Level Additional Maths 4037 past papers, counted from every paper since 2004.