Cho các đa thức A = 3x4  2x3  x + 1; B = 2x3 + 4x2 + 5x và C = 3x4 + 2x2 + 5. Tính A + B + C; A  B + C và A  B  C.

A + B = (3x⁴ - 2x³ - x + 1) + (-2x³ + 4x² + 5x)

           = 3x⁴ - 2x³ - x + 1 - 2x³ + 4x² + 5x

           = 3x⁴ + (- 2x³ - 2x³) + 4x² + (- x + 5x) + 1

           = 3x⁴ - 4x³ + 4x² + 4x + 1.

A + B + C = (A + B) + C

                 = (3x⁴ - 4x³ + 4x² + 4x + 1) + (-3x⁴ + 2x² + 5)

                 = 3x⁴ - 4x³ + 4x² + 4x + 1 - 3x⁴ + 2x² + 5

                 = (3x⁴ - 3x⁴) - 4x³ + (4x² + 2x²) + 4x + (1 + 5)

                 = - 4x³ + 6x² + 4x + 6.

A – B = (3x⁴ - 2x³ - x + 1) – (-2x³ + 4x² + 5x)

           = 3x⁴ - 2x³ - x + 1 + 2x³ – 4x² – 5x

           = 3x⁴ + (- 2x³ + 2x³) – 4x² + (- x – 5x) + 1

           = 3x⁴ – 4x² – 6x + 1.

A - B + C = (A – B) + C

                 = (3x⁴ – 4x² – 6x + 1) + (-3x⁴ + 2x² + 5)

                 = 3x⁴ – 4x² – 6x + 1 - 3x⁴ + 2x² + 5

                 = (3x⁴ - 3x⁴) + (-4x² + 2x²) – 6x + (1 + 5)

                 = -2x² - 6x + 6.

A - B - C = (A – B) – C

                 = (3x⁴ – 4x² – 6x + 1) - (-3x⁴ + 2x² + 5)

                 = 3x⁴ – 4x² – 6x + 1 + 3x⁴ - 2x² - 5

                 = (3x⁴ + 3x⁴) + (- 4x² - 2x²) – 6x + (1 - 5)

                 = 6x⁴ - 6x² - 6x - 4.

Vậy A + B + C = -4x³ + 6x² + 4x + 6; A - B + C = -2x² - 6x + 6;

A - B - C = 6x⁴ - 6x² - 6x - 4.