The binomial theorem
The coefficients of (a + b)ⁿ are row n of Pascal's triangle, and the (k + 1)th term is C(n, k)·aⁿ⁻ᵏ·bᵏ.
A worked example
The term containing x² in (x + 2)⁵: x² needs 5 − k = 2, so k = 3. The coefficient is C(5, 3) × 2³ = 10 × 8 = 80, so the term is 80x².
The mistake people actually make
Count from k = 0: the third term has k = 2. Raise the whole second term, sign and coefficient included.