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Easy: (x + b)³ and (x + b)⁴
The binomial theorem gives (a + b)ⁿ as a sum of terms C(n, k)·aⁿ⁻ᵏ·bᵏ, where the coefficients C(n, k) are the numbers in row n of Pascal's triangle. The powers of the first term count down from n while the powers of the second count up from 0. To find one term, pick the k that gives the right power of x.
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They are the numbers in row n of Pascal's triangle, also written C(n, k). For (a + b)⁴ they are 1, 4, 6, 4, 1.
The term with bᵏ is C(n, k) aⁿ⁻ᵏ bᵏ. In (2x + 1)⁵, the x³ term uses k = 2: C(5, 2)(2x)³(1)² = 10 × 8x³ = 80x³.
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