WAEC 2023 · Paper 1 · Q23

Find the fifth term in the binomial expansion of $(q + x)^7$ .

Worked solution (try it first)

The $(r + 1)$ th term of $(q + x)^n$ is $^{n}C_r\, q^{n - r} x^r$ , so the fifth term has $r = 4$ .
$^{7}C_4 = 35$ , and the powers are $q^{7 - 4} = q^3$ and $x^4$ .
So the fifth term is $35q^3x^4$ , option C.