Binomial Expansion (Edexcel A-Level Mathematics): Flashcards

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

$n$ choose $k = n! / (k!(n-k)!)$

Binomial coefficient, $x$ power, and $y$ power.

$(x + y)^2 = x^2 + 2xy + y^2$

$(x + 1)^3 = x^3 + 3x^2 + 3x + 1$

The total number of terms is $n + 1$.

Each number is the sum of the two above; rows give coefficients.

The term is given by $C(n, k)(a^{n-k})(b^k)(-1)^k$.

It provides coefficients for binomial distributions.

$4$ choose $2$ = $6$ ways.