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在对含有多个字母的代数式进行变形时,适当地确立一个字母作“元”。并按这个“元”来分析,可使一些数学问题得到规范化和简单的解法。一分解因式中按元分组 [例1] 把a~4(b-c)+b~4(c-a)+c~4(a-b)分解因式略解:原式=(b-c)a~4+(c~4-b~4)a+bc(b~3-c~3)<以a为元> =(6-c)(a~4-ab~3-ac~3-abc~2-ab~2c+b~3c+bc~3+b~2c~2) =(6-c)[(c-a)b~3+(c~2-ac)b~2+(c~3-ac~2)b+(a~4-ac~3)]<以6为元> =(6-c)(c-a)(b~3+cb~2+c~2b-a~3-ac~23-a~2c)
When deforming an algebraic expression containing multiple letters, one letter is properly established as a “meta.” According to this “meta” analysis, some mathematical problems can be standardized and simple solutions. A decomposition factor according to the grouping [Example 1] to a ~ 4 (bc) + b ~ 4 (ca) + c ~ 4 (ab) decomposition factor slightly solved: the original = (bc) a ~ 4 + (c ~4-b~4)a+bc(b~3-c~3)(6-c)(a~4-ab~3-ac~3-abc~2-ab~ 2c+b~3c+bc~3+b~2c~2) =(6-c)[(ca)b~3+(c~2-ac)b~2+(c~3-ac~2) b+(a~4-ac~3)](6-c)(ca)(b~3+cb~2+c~2b-a~3-ac~23-a~2c )