Quick questions on The binomial theorem explained: O-Level A-Maths

The expansion of $(a + b)^n$ has $n + 1$ terms. In each term the powers of $a$ and $b$ add to $n$: $a$ starts at power $n$ and falls to $0$, while $b$ rises from $0$ to $n$:

The coefficient $\binom{n}{r}$ (read "n choose r") counts the terms and is given by:

Each row of Pascal's triangle is symmetric: $\binom{n}{r} = \binom{n}{n-r}$, so the coefficients read the same forwards and backwards. This is a useful check, since a row that is not symmetric has an error, and it lets you write the second half of a long row from the first.

$(a + b)^n$ has $n + 1$ terms; missing one usually means a dropped coefficient.

Write down the binomial coefficients for $(a + b)^5$. [1 mark]

Expand $(1 + x)^3$. [2 marks]

Find the first three terms of $(2 - x)^4$ in ascending powers of $x$. [3 marks]