New Zealand
Level 8 - NCEA Level 3

# Binomial Expansions and Coefficients

## Interactive practice questions

Evaluate $\binom{6}{5}$(65).

Easy
Approx a minute

Evaluate $\binom{14}{1}$(141).

How many terms does the expansion of $\left(9x+6y\right)^8$(9x+6y)8 have?

The $3$3rd row of Pascal’s triangle contains the elements $1$1, $3$3, $3$3, $1$1. Each of these can be rewritten in $\nCr{n}{r}$nCr form: $\nCr{3}{0}$3C0, $\nCr{3}{1}$3C1, $\nCr{3}{2}$3C2, $\nCr{3}{3}$3C3.

Rewrite each element of the $5$5th row of Pascal’s triangle as an $\nCr{n}{r}$nCr coefficient.

### Outcomes

#### M8-3

Use permutations and combinations