m(a b-c) = ma mb-mc (a b)(a-b) = a^2-b^2 (x a)(x b) = x^2 (a b)x ab (a b)(c d) = ac ad bc bd (a±b)^2 = a^2 ±2ab b^2 (a b c)^2 = a^2 b^2 c^2 2ab 2bc 2ac a^4 a^2*b^2 b^4 = (a^2 b^2)^2-a^2*b^2 = (a^2 ab b^2)(a^2-ab b^2) Helen-秦九韶公式: p=(a b c)/2, S△ = 1/2*√[(a*b)^2-((a^2 b^2-c^2)/2)^2] = √[p*(p-a)*(p-b)*(p-b)] |a bi||c di| =|(a bi)(c di)| , i^2=-1 (a^2 b^2)(c^2 d^2)=(ac-bd)^2 (ad bc)^2 =(ad-bc)^2 (ac bd)^2 // 上式中 b*√n -->b ，d*√n -->d (a^2 n*b^2)(c^2 n*d^2)=(ac-n*bd)^2 n*(ad bc)^2 =(ac n*bd)^2 n*(ad-bc)^2 a^3 b^3 = (a b)(a^2-ab b^2) a^3 -b^3 =(a-b)(a^2 ab b^2) //上式中用-b代入b即得此式 (a b)^3 = a^3 b^3 3ab(a b) a^3 b^3 c^3-3abc = (a b c)(a^2 b^2 c^2-ab-bc-ca)

Euler's four-square identity :

Lagrange's identity：

你可以在sagecell中进行实验, 相关的函数有 expand,simplify,factor......