ESEMPI:

1. Siano f(x) = 1 + x = 1 + 1x + 0x² e g(x) = 3 – 2x + x².

f (x)+ g(x) = (1 + 3) + (1 - 2)x + (0 + 1)x² = 4 – x + x².

2. Sia f(x) = 1 + x- x² e g(x) = 2 + x² + x³.

Quindi a₀ = 1, a₁ = 1, a₂ = -1, a₃ = a₄ = … = 0

b₀ = 2, b₁ = 0, b₂ = 1, b₃ = 1, b₄ = b₅ = … = 0.

Così: c₀ = a₀b₀ = 1 * 2 = 2, c₁ = a₁ b₀ + a₀ b₁ = 1 * 2 + 1 * 0 = 2,

c₂ = a₂ b₀ + a₁ b₁ + a₀ b₂ = (-1) * 2 + 1 * 0 + 1 * 1 = -1,

c₃ = a₃ b₀ + a₂ b₁ + a₁ b₂ + a₀ b₃ = 0 * 2 + (-1) * 0 + 1 * 1 + 1 * 1 = 2,

c₄ = a₄ b₀ + a₃ b₁ + a₂ b₂ + a₁ b₃ + a₀ b₄ = 0 * 2 + 0 * 0 + (-1) * 1 + 1 * 1 + 1 * 0 = 0,

c₅ = a₅ b₀ + a₄ b₁ + a₃ b₂ + a₂ b₃ + a₁ b₄ + a₀ b₅ =

= 0 * 2 + 0 * 0 + 0 * 1 + (-1) * 1 + 1 * 0 + 0 * 0 = -1,

c₆ = a₆ b₀ + a₅ b₁ + a₄ b₂ + a₃ b₃ + a₂ b₄ + a₁ b₅ + a₀ b₆ =

= 0 * 2 + 0 * 0 + 0 * 1 + 0 * 1 + (-1) * 0 + 1 * 0 + 1 * 0 = 0,

c₇ = c₈ = … = 0.

Allora:

f(x)g(x) = h(x) = 2 + 2x – x² + 2x³ – x⁵.