Tính hiệu P(x) - Q(x) bằng hai cách, trong đó: P(x) = 6x^3 + 8x^2 + 5x - 2; Q(x) = -9x^3 + 6x^2 + 3 + 2x.

Cách 1. Tính hiệu theo hàng ngang:

P(x) - Q(x) = 6x³ + 8x² + 5x - 2 - (-9x³ + 6x² + 3 + 2x)

= 6x³ + 8x² + 5x - 2 + 9x³ - 6x² - 3 - 2x

= (6x³ + 9x³) + (8x² - 6x²) + (5x - 2x) + (-2 - 3)

= 15x³ + 2x² + 3x - 5.

Vậy P(x) - Q(x) = 15x³ + 2x² + 3x - 5.

Cách 2. Tính hiệu theo cột dọc:

Q(x) = -9x³ + 6x² + 3 + 2x = -9x³ + 6x² + 2x + 3.

$\begin{array}{l}-\underset{¯}{\begin{array}{c}\begin{array}{l}6{\text{x}}^3\\ -9{\text{x}}^3\end{array}\end{array}\begin{array}{c}\begin{array}{l}+\\ +\end{array}\end{array}\begin{array}{c}\begin{array}{l}8{\text{x}}^2\\ 6{\text{x}}^2\end{array}\end{array}\begin{array}{c}\begin{array}{l}+\\ +\end{array}\end{array}\begin{array}{c}\begin{array}{l}5\text{x}\\ 2\text{x}\end{array}\end{array}\begin{array}{c}\begin{array}{l}-\\ +\end{array}\end{array}\begin{array}{c}\begin{array}{l}2\\ 3\end{array}\end{array}}\\ 15x^3+2{\text{x}}^2+3\text{x}-5\end{array}$

Vậy P(x) - Q(x) = 15x³ + 2x² + 3x - 5.