使用二项式公式计算

几何画板及绘图内容加载中，请稍等……

2024-07-01 17:15

函数

所属专题 Binomische Formeln

①本范例演示如何使用二项式公式计算代数表达式的幂；②涉及的核心数学概念包括二项式定理、代数运算、表达式化简；③作图要点——从下方『构造摘要』提炼用到了Expand(展开式), Text(文本显示), Flatten(展平列表), Random(随机数生成), Sequence(序列生成), Join(连接字符串), SelectedIndex(选择索引), If(条件判断), Element(元素选择), Textfield(文本输入框), Invert(反转列表)等GeoGebra命令/对象；④适合的学段或用途——本范例适合7-8年级学生，用于练习和巩固二项式定理的应用，通过交互式操作加深理解。

GeoGebra 命令及参数

Expand(TaskFunc) → solFunc
Text(inputFunc) → txtInput
Flatten(Join[{{1, 1, 2, 2, 3, 3}, Sequence[Shuffle[1…3], k, 1, 34]}]) → CaseList
Random(1, 12, 100) → ParList1, {1, 5, 7, 8, 11, 7, 7, 2, 7, 9, 4, 4, 9, 7, 12, 8, 1, 4, 9, 8, 2, 7, 9, 10, 12, 7, 11, 10, 1, 9, 6, 8, 6, 5, 9, 3, 11, 6, 12, 10, 9, 7, 7, 11, 8, 6, 8, 2, 1, 10, 3, 8, 4, 6, 3, 7, 3, 1, 8, 7, 4, 5, 5, 11, 6, 2, 4, 6, 4, 4, 4, 10, 2, 5, 11, 3, 1, 5, 4, 4, 5, 4, 12, 7, 9, 3, 2, 11, 11, 12, 5, 6, 11, 11, 11, 6, 12, 6, 7, 9}
Sequence(RandomElement[Remove[1…12, {ParList1(k)}]], k, 1, 100) → ParList2, {9, 2, 5, 5, 2, 3, 10, 6, 3, 12, 8, 12, 7, 11, 7, 5, 4, 2, 2, 7, 7, 10, 7, 8, 7, 6, 1, 7, 7, 5, 7, 12, 9, 7, 12, 5, 3, 8, 11, 7, 5, 8, 5, 10, 5, 7, 10, 1, 4, 11, 8, 1, 10, 2, 6, 3, 10, 10, 7, 10, 9, 7, 4, 12, 11, 9, 10, 3, 3, 8, 9, 3, 12, 12, 9, 4, 5, 10, 8, 6, 8, 7, 8, 1, 7, 10, 4, 10, 3, 1, 8, 7, 8, 8, 5, 1, 6, 8, 9, 7}
Sequence(RandomElement[Alphabet], k, 1, 100) → VarList1, {"s", "e", "w", "z", "s", "z", "q", "e", "f", "d", "x", "t", "z", "g", "j", "c", "x", "r", "j", "f", "e", "c", "q", "y", "t", "d", "d", "h", "u", "i", "j", "y", "u", "r", "f", "d", "v", "j", "r", "f", "d", "d", "j", "v", "f", "s", "z", "d", "v", "t", "s", "s", "y", "e", "g", "h", "f", "j", "z", "y", "g", "h", "r", "y", "w", "c", "h", "z", "r", "s", "h", "g", "g", "h", "v", "q", "d", "i", "g", "r", "f", "f", "z", "y", "z", "z", "u", "d", "x", "j", "v", "u", "z", "h", "w", "e", "s", "f", "s", "w"}
Random(1, 3, 100) → CaseVarList, {1, 1, 3, 3, 3, 2, 2, 2, 2, 3, 1, 2, 3, 2, 1, 3, 3, 2, 3, 1, 1, 2, 2, 3, 3, 3, 3, 1, 2, 1, 1, 3, 1, 3, 2, 2, 1, 2, 2, 3, 1, 1, 1, 1, 3, 1, 3, 3, 1, 1, 2, 2, 3, 1, 1, 2, 3, 2, 1, 3, 1, 3, 2, 3, 1, 1, 3, 2, 2, 2, 1, 3, 1, 3, 2, 1, 1, 1, 3, 1, 2, 3, 1, 1, 1, 3, 3, 2, 1, 2, 2, 3, 3, 2, 2, 3, 1, 3, 3, 3}
Sequence(RandomElement[Remove[Alphabet, {VarList1(k)}]], k, 1, 100) → VarList2, {"y", "v", "x", "h", "t", "e", "c", "w", "c", "x", "z", "i", "c", "j", "y", "v", "q", "s", "d", "h", "d", "f", "g", "s", "d", "v", "i", "u", "z", "t", "c", "c", "i", "i", "s", "r", "u", "h", "c", "r", "s", "i", "t", "y", "s", "x", "j", "q", "e", "f", "g", "w", "g", "r", "q", "c", "u", "z", "j", "u", "e", "c", "d", "r", "c", "g", "q", "i", "f", "h", "x", "u", "y", "u", "c", "w", "t", "z", "v", "h", "h", "v", "v", "h", "j", "u", "r", "r", "f", "t", "e", "e", "w", "g", "q", "r", "g", "q", "y", "j"}
Sequence(Shuffle[1…3], k, 1, 100) → OrderList1, {{2, 1, 3}, {2, 1, 3}, {3, 1, 2}, {2, 1, 3}, {1, 2, 3}, {1, 2, 3}, {3, 2, 1}, {2, 3, 1}, {2, 3, 1}, {1, 2, 3}, {3, 1, 2}, {1, 2, 3}, {3, 1, 2}, {3, 1, 2}, {1, 2, 3}, {3, 1, 2}, {1, 3, 2}, {3, 2, 1}, {1, 3, 2}, {2, 3, 1}, {3, 2, 1}, {2, 1, 3}, {3, 2, 1}, {3, 1, 2}, {2, 3, 1}, {3, 2, 1}, {2, 1, 3}, {2, 3, 1}, {1, 3, 2}, {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {3, 1, 2}, {2, 3, 1}, {2, 1, 3}, {1, 2, 3}, {2, 1, 3}, {2, 1, 3}, {1, 3, 2}, {1, 3, 2}, {3, 1, 2}, {1, 3, 2}, {2, 1, 3}, {3, 2, 1}, {1, 2, 3}, {1, 2, 3}, {2, 3, 1}, {1, 3, 2}, {2, 3, 1}, {2, 3, 1}, {2, 3, 1}, {3, 2, 1}, {2, 3, 1}, {1, 3, 2}, {2, 3, 1}, {1, 2, 3}, {3, 2, 1}, {3, 1, 2}, {2, 1, 3}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1}, {2, 1, 3}, {2, 1, 3}, {3, 2, 1}, {1, 3, 2}, {2, 3, 1}, {1, 3, 2}, {2, 3, 1}, {3, 2, 1}, {1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {1, 3, 2}, {1, 2, 3}, {3, 2, 1}, {2, 3, 1}, {1, 2, 3}, {3, 1, 2}, {2, 1, 3}, {1, 2, 3}, {3, 2, 1}, {3, 1, 2}, {1, 2, 3}, {2, 3, 1}, {1, 3, 2}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1}, {1, 2, 3}, {2, 3, 1}, {1, 2, 3}, {3, 1, 2}, {3, 2, 1}, {2, 3, 1}, {3, 1, 2}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}, {3, 1, 2}}
Sequence(Shuffle[1…3], k, 1, 100) → OrderList2, {{3, 2, 1}, {3, 1, 2}, {1, 2, 3}, {1, 3, 2}, {1, 3, 2}, {1, 3, 2}, {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {3, 2, 1}, {1, 2, 3}, {1, 3, 2}, {2, 3, 1}, {3, 1, 2}, {1, 3, 2}, {2, 3, 1}, {3, 1, 2}, {3, 1, 2}, {3, 2, 1}, {2, 1, 3}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {1, 3, 2}, {3, 2, 1}, {2, 3, 1}, {1, 3, 2}, {3, 1, 2}, {2, 1, 3}, {2, 3, 1}, {2, 1, 3}, {1, 3, 2}, {1, 2, 3}, {1, 2, 3}, {2, 1, 3}, {1, 2, 3}, {1, 3, 2}, {3, 1, 2}, {3, 1, 2}, {1, 3, 2}, {1, 2, 3}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1}, {2, 1, 3}, {3, 1, 2}, {3, 1, 2}, {2, 1, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {2, 1, 3}, {1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {3, 2, 1}, {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 1, 3}, {3, 2, 1}, {2, 1, 3}, {1, 3, 2}, {3, 1, 2}, {1, 2, 3}, {2, 3, 1}, {1, 2, 3}, {2, 1, 3}, {3, 2, 1}, {1, 2, 3}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}, {3, 2, 1}, {1, 3, 2}, {1, 2, 3}, {1, 3, 2}, {2, 3, 1}, {1, 2, 3}, {1, 2, 3}, {2, 1, 3}, {1, 2, 3}, {2, 1, 3}, {2, 1, 3}, {3, 2, 1}, {3, 1, 2}, {2, 3, 1}, {3, 1, 2}, {3, 1, 2}, {1, 3, 2}, {2, 3, 1}, {1, 3, 2}, {1, 3, 2}, {3, 1, 2}, {1, 2, 3}, {2, 1, 3}, {2, 1, 3}, {3, 1, 2}, {2, 1, 3}, {1, 2, 3}}
Sequence(Shuffle[1…3], k, 1, 100) → OrderList3, {{1, 3, 2}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}, {1, 3, 2}, {2, 3, 1}, {1, 2, 3}, {3, 1, 2}, {1, 3, 2}, {1, 2, 3}, {1, 2, 3}, {2, 3, 1}, {3, 2, 1}, {1, 3, 2}, {2, 1, 3}, {3, 1, 2}, {2, 3, 1}, {2, 1, 3}, {1, 2, 3}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}, {1, 3, 2}, {2, 3, 1}, {1, 2, 3}, {1, 3, 2}, {1, 2, 3}, {3, 1, 2}, {3, 2, 1}, {2, 3, 1}, {2, 1, 3}, {3, 1, 2}, {1, 3, 2}, {3, 1, 2}, {2, 1, 3}, {1, 2, 3}, {1, 3, 2}, {3, 2, 1}, {3, 1, 2}, {3, 1, 2}, {3, 2, 1}, {2, 3, 1}, {3, 1, 2}, {3, 1, 2}, {3, 2, 1}, {1, 3, 2}, {2, 3, 1}, {2, 3, 1}, {2, 1, 3}, {1, 3, 2}, {2, 1, 3}, {1, 2, 3}, {2, 3, 1}, {3, 1, 2}, {1, 3, 2}, {3, 1, 2}, {2, 3, 1}, {1, 2, 3}, {1, 3, 2}, {1, 2, 3}, {1, 2, 3}, {2, 1, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 2, 1}, {3, 2, 1}, {2, 3, 1}, {1, 2, 3}, {2, 1, 3}, {1, 2, 3}, {3, 1, 2}, {2, 1, 3}, {1, 3, 2}, {3, 2, 1}, {2, 1, 3}, {1, 2, 3}, {1, 3, 2}, {3, 2, 1}, {1, 2, 3}, {2, 3, 1}, {1, 3, 2}, {1, 3, 2}, {2, 3, 1}, {1, 3, 2}, {2, 3, 1}, {1, 3, 2}, {1, 2, 3}, {2, 3, 1}, {1, 3, 2}, {1, 2, 3}, {2, 3, 1}, {1, 3, 2}, {3, 1, 2}, {1, 3, 2}, {3, 2, 1}}
Join({{"$\textsf{\phantom{144\:b² }\vphantom{gb²}}$"}, {(("$\textsf{" * DDList1(Order1(1))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList1(Order1(2))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList1(Order1(3))) * "\vphantom{gb²}}$")}}) → dropdown1
Join({{"$\textsf{\phantom{144\:b² }\vphantom{gb²}}$"}, {(("$\textsf{" * DDList3(Order3(1))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList3(Order3(2))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList3(Order3(3))) * "\vphantom{gb²}}$")}}) → dropdown3
Join({{"$\textsf{\phantom{144\:b² }\vphantom{gb²}}$"}, {(("$\textsf{" * DDList2(Order2(1))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList2(Order2(2))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList2(Order2(3))) * "\vphantom{gb²}}$")}}) → dropdown2
SelectedIndex(dropdown1) → indexdd1
SelectedIndex(dropdown2) → indexdd2
SelectedIndex(dropdown3) → indexdd3
SelectedIndex(dropdownSign1) → indexddS1
SelectedIndex(dropdownSign2) → indexddS2
If(Case ≠ 3, indexdd2 - 1 ≟ IndexOf[1, Order2], true) → correctdd2
If(Case ≠ 3, indexddS2 ≟ 2, true) → correctddS2
If(step ≟ 1, correctExtend ∧ correctValue, correctdd1 ∧ correctdd2 ∧ correctdd3 ∧ correctddS1 ∧ correctddS2) → correct
Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {6, 10, 7, 8, 6, 8, 8, 6, 1, 10}
Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
If(step ≟ 1, Defined[inputFunc], indexdd1 ≠ 1 ∧ If[Case ≟ 3, true, indexdd2 ≠ 1] ∧ indexdd3 ≠ 1 ∧ indexddS1 ≠ 1 ∧ If[Case ≟ 3, true, indexddS2 ≠ 1]) → clickableBtnValidate
Join(Sequence[Shuffle[1…5], k, 1, 20]) → KidsList
Textfield(inputFunc) → inputBox
If(CaseVar ≟ 2, "", var1) → txtVar1
If(CaseVar ≟ 1, "", var2) → txtVar2
Invert(pixMat) → invPixMat
If(Case ≟ 3, PosDDS1 + (1.42, 0), PosDDS2 + (1.42, 0)) → PosDD3

AI 绘图提示语参考

画一个包含100个随机多项式的展开式，每个多项式由随机字母和数字组成，展示展开式的结果，并允许用户选择多项式进行验证。首先创建100个随机字母和数字，然后随机生成多项式，展示在下拉菜单中，用户选择多项式后，系统验证选择是否正确。

以上提示语为根据原始绘图命令整理而来，仅供参考。