The binomial expansion
Watch the whole lecture free
Make a free account to watch every lecture to the end: 6 worked examples, 5 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
That was the teaching part. The rest of this lecture is free with an account: 6 worked examples, 5 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
No password needed now: we email you a link to set one. Already have an account? Sign in, then come back to this page.
The teaching part (1 min) is free to watch. A free account opens the whole lecture: 6 worked examples, 5 practice questions, 1 real past-paper question with the answer 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: Finding a constant in a product.
The whole chapter: Series.
Chapter 1.6: Series
Also for A Level Maths 9709 Paper 1
Which topics come up most in A Level Maths 9709 Paper 1 past papers, counted from every paper since 2004.