CAIE: A Level - Mathematics 9709 - Pure Mathematics 1

Binomial Expansion / Expansion of Three Terms

KEYPOINTS:

n! = n(n – 1)(n – 2)(n – 3) … (n – r) … (3) (2) (1)
ⁿC_r = \(\frac{n!}{ r!(n – r)!}\)
(a + b)ⁿ = aⁿ + ⁿC₁a^n–1b + ⁿC₂a^n–2b² + … + ⁿC_ra^n–rb^r + …
\((1 + b)^n = 1 + nb + \frac{n(n – 1)}{2!} b^2 + \frac{n(n – 1)(n – 2)}{3!} b^3 + \cdots\)
\((a+b)^n = a^n + na^{n – 1}b + \frac{n(n – 1)}{2!}a^{n – 2}b^2 + \frac{n(n – 1)(n – 2)}{3!}a^{n – 3}b^3 + \cdots\)

Past Papers Topic Wise Questions A Level: Mathematics 9709 - Pure Mathematics 1 Binomial Expansion | Expansion of Three Terms

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