多項式的加減運算_直式計算分離係數法

例

$\begin{array} {cl} & (6+3x-4x^2)+(5x^2-3x+1) \\ = & (-4x^2+3x+6)+(5x^2-3x+1) \end{array}$

$\begin{array} {rrrr} & x^2\text{項} & x\text{項} & \text{常數項} \\ & -4 & +3 & +6 \\ +) & +5 & -3 & +1 \\\hline & +1 & +0 & +7 \end{array}$

$\Rightarrow x^2+7$

例

$\begin{array} {cl} & (x^2+4x-6)-(2-3x^2) \\ = & (x^2+4x-6)-(-3x^2+0x+2) \end{array}$

$\begin{array} {rrrr} & x^2\text{項} & x\text{項} & \text{常數項} \\ & +1 & +4 & -6 \\ -) & -3 & +0 & +2 \\\hline & +4 & +4 & -8 \end{array}$

$\Rightarrow 4x^2+4x-8$