General Binomial Expansion (Edexcel A-Level Mathematics): Flashcards

$(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k$

$\binom{n}{r} = \frac{n!}{r!(n-r)!}$

$(1 + x)^n = \sum_{k=0}^{\infty} \binom{n}{k} x^k$ for $|x|<1$

$1 - 3x + 3x^2 - x^3$

$\frac{1}{13,983,816}$ (choosing $6$ from $49$)

The constant term is 64 from $(2^6)$.

Term = $\binom{n}{k} a^{(n-k)} b^k$

The first term is 81, from $(3)^4 = 81$.

Coefficient = $C(12, 6) \times (2^6) = 924 \times 64 = 59136$

$1 + 12x + 60x^2 + 80x^3 + ...$