Find the coefficient of x⁷ in the expansion of (x² + 2/x)⁸.

Step 1. The general term. $T_{r+1} = {}^8C_r\,x^{2(8-r)}\,2^r\,x^{-r} = {}^8C_r\,2^r\,x^{16-3r}$.

Step 2. Match the power. $16 - 3r = 7$ gives $r = 3$, a whole number between $0$ and $8$.

Step 3. The coefficient. ${}^8C_3 \times 2^3 = 56 \times 8 = 448$.