Cho hai đa thức P(x) = 2x^3 - 9x^2 + 5 và Q(x) = -2x^2 - 4x^3 + 7x. Hãy tính P(x) - Q(x) bằng hai cách.

Cách 1:

P(x) - Q(x) = (2x³ - 9x² + 5) - (-2x² - 4x³ + 7x)

P(x) - Q(x) = 2x³ - 9x² + 5 + 2x² + 4x³ - 7x

P(x) - Q(x) = (2x³ + 4x³) + (-9x² + 2x²) - 7x + 5

P(x) - Q(x) = 6x³ - 7x² - 7x + 5

Vậy P(x) - Q(x) = 6x³ - 7x² - 7x + 5.

Cách 2:

Q(x) = -2x² - 4x³ + 7x = - 4x³ - 2x² + 7x

Khi đó thực hiện đặt phép tính ta có:

$\begin{array}{l}-\underset{¯}{\begin{array}{c}\begin{array}{l}\\ -\end{array}\end{array}\begin{array}{c}\begin{array}{l}2{\text{x}}^3\\ 4{\text{x}}^3\end{array}\end{array}\begin{array}{c}\begin{array}{l}-\\ -\end{array}\end{array}\begin{array}{c}\begin{array}{l}9{\text{x}}^2\\ 2{\text{x}}^2\end{array}\end{array}\begin{array}{c}\begin{array}{l}\\ +\end{array}\end{array}\begin{array}{c}\begin{array}{l}\\ 7\text{x}\end{array}\end{array}\begin{array}{c}\begin{array}{l}+\\ \end{array}\end{array}\begin{array}{c}\begin{array}{l}5\\ \end{array}\end{array}}\\ 6{\text{x}}^3-7{\text{x}}^2-7\text{x}+5\end{array}$

Vậy P(x) - Q(x) = 6x³ - 7x² - 7x + 5.