Mathematics (AS)·Sequences and series · NSSCAS 1.2.1
The binomial expansion
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Ever wondered how to expand a bracket like (x + 2)⁴ without multiplying it out four painful times? In this lesson Miss Eve shows you the binomial expansion — the beautiful shortcut built from factorials, the ⁿCᵣ notation and Pascal's triangle. You will expand brackets to any positive whole-number power, handle sneaky minus signs, and pick out a single coefficient the fast exam way. By the end, this favourite NSSCAS Paper 1 question will feel like free marks.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 1.2.1):
- Use the expansion of (a + b)ⁿ, where n is a positive integer, to expand binomials completely and accurately.
- Know and use the notations ⁿCᵣ (also written (n r)) and n!, evaluating them by hand and with the calculator's nCr button.
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Miss Eve and Mike talk through the whole topic — with the figure and working drawn live.