2次式の因数分解
- $ax^2+bx+c=(\alpha x+\beta)(\gamma x+\delta)$，ただし，$a=\alpha+\gamma$，$b=\alpha\delta+\beta\gamma$，$c=\beta\delta$
- $x^2+2xy+y^2=(x+y)^2$
- $x^2-2xy+y^2=(x-y)^2$
- $x^2-y^2=(x+y)(x-y)$
3次式の因数分解
- $x^3+3x^2y+3xy^2+y^3=(x+y)^3$
- $x^3-3x^2y+3xy^2-y^3=(x-y)^3$
- $x^3+y^3=(x+y)(x^2-xy+y^2)$
- $x^3-y^3=(x-y)(x^2+xy+y^2)$
4次式の因数分解
- $x^4+x^2+1=(x^2+x+1)(x^2-x+1)$