The Binomial Theorem (VCE SSCE Mathematical Methods): Flashcards

Algebraic expression with two terms

$n+1$ terms

Sum of two numbers directly above it

Ways to choose $r$ objects from $n$ objects

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

$5 \times 4 \times 3 \times 2 \times 1 = 120$

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

$\binom{n}{r}(ax)^{n-r}b^r$

Decreasing powers of $x$

$r=7$ (use $r+1$ for term position)