tiwe0/geochat/factorization-formulas

Claude Code and agent skill by tiwe0/geochat

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因式分解、乘法公式、配方和代数结构识别的二级技能。

Install

npx vskill@latest install tiwe0/geochat/factorization-formulas

SKILL.md

因式分解与公式

用于提公因式、平方差、完全平方、二次三项式、分组分解和配方。只处理代数结构；若目标是求方程根，转交 quadratic-equation。

工作顺序：

  1. 先检查公因式、次数、项数和特殊系数。
  2. 判断是否符合平方差、完全平方或二次三项式结构。
  3. 分解后回乘验证，避免符号错误。
  4. 配方题要说明加减同一个量的原因。

关键规则：先提最大公因式；a^2-b^2=(a-b)(a+b)，而平方和在有理数范围通常不可分；完全平方中间项必须是 ±2ab；分解结果应与原式同定义域并通过 Expand 回乘。

原生输入小例子

此技能当前不声明自动执行 GeoGebra 的工具；以下输入用于模型校验、讲解或用户手动演示，不扩展工具配置。在空白构图中逐行输入；名称冲突时改名，不覆盖用户对象。

ggb
sourceFac = x^2 - 5*x + 6
factoredFac = Factor(sourceFac)
roundTripFac = Expand(factoredFac)
residualFac = roundTripFac - sourceFac
irreducibleFac = Factor(x^2 + 1)

预期：factoredFac=(x-2)(x-3)，roundTripFac=x^2-5x+6，residualFac=0；irreducibleFac 在有理数范围保持 x^2+1。正常验证检查回乘；退化验证检查常数、多项式零项或平方和；边界验证要声明所用数域，不能把复数分解冒充实数/有理数分解。

官方参考：Factor、Expand、CompleteSquare。Factor 会加载 CAS，避免为纯展示重复调用。

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