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Polynomial Multiplication Demo

Polynomial Multiplication Demo
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2015-09-25 23:32
FunctionCalculusGeometric ConstructionGraphing
In collections CCSS Support Math II Unit 2
This example demonstrates how to use GeoGebra to calculate and simplify the product of [math]2x[/math] and [math](3x – y)[/math]. Core math concepts include polynomial multiplication and simplification. Key GeoGebra commands and objects used are Segment, Sequence, LaTeX, Vector, along with Calc, Hint, Next, Grey_Prev, Grey_next, Prev, steps, Progressbar, A_0, stepmax, B_0, Scaleline, list1, list2, list3, Scalevalue0, Scalevalue1, p, q, Scalevalue2, Scalevalue3, Scalevalue4, Scalevalue5, Scalevalue6, Scalevalue7, Scalevalue8, Scalevalue9, Scalevalue10, Multiplier, C_0, D_0, j, u, Random, Original, DummyDatakit, Words, Datakit_Close, Hint_Close, Border. Suitable for middle school students and above learning polynomial operations and GeoGebra usage.

GeoGebra Commands & Parameters

  1. Segment(A_0, B_0) → Scaleline
  2. Sequence(Segment[A_0 + (i, 0), A_0 + (i, (-0.5))], i, 0, 10) → list1
  3. Sequence(Segment[A_0 + (i - 0.5, 0), A_0 + (i - 0.5, (-0.4))], i, 1, 10) → list2
  4. Sequence(Sequence[Segment[A_0 + ((0.5 * i) + (0.1 * j), 0), A_0 + ((0.5 * i) + (0.1 * j), (-0.3))], j, 1, 4], i, 0, 19) → list3
  5. LaTeX("\text{0}") → Scalevalue0
  6. LaTeX("\text{1}") → Scalevalue1
  7. LaTeX("\text{2}") → Scalevalue2
  8. LaTeX("\text{3}") → Scalevalue3
  9. LaTeX("\text{4}") → Scalevalue4
  10. LaTeX("\text{5}") → Scalevalue5
  11. LaTeX("\text{6}") → Scalevalue6
  12. LaTeX("\text{7}") → Scalevalue7
  13. LaTeX("\text{8}") → Scalevalue8
  14. LaTeX("\text{9}") → Scalevalue9
  15. LaTeX("\text{10}") → Scalevalue10
  16. Segment(D_0, (x(D_0), 0)) → j
  17. Vector(C_0, D_0) → u
  18. LaTeX("\text{Use the Distributive Property to find the product of the two expressions.}") → text2
  19. LaTeX("\text{by each term in the second expression.}") → text5
  20. LaTeX("\text{Apply the Distributive Property.}") → text9
  21. LaTeX("\text{Simplify the multiplication.}") → text12
  22. LaTeX("\text{Simplify.}") → text13
  23. LaTeX("\text{Combine the like terms.}") → text15
  24. LaTeX((("\text{Thus, to apply the Distributive Property in order to multiply the expressions, multiply the first expression, \textcolor{#000099}{" * Multiplier) * "x},}")) → text4
  25. LaTeX((("\text{Multiply \textcolor{#000099}{" * Multiplier) * "x} by each term in the second expression.}")) → text7
  26. Segment((0, 0), (0, 1.6)) → i
  27. Segment(F_0, (x(F_0), 0)) → k
  28. Vector(E_0, F_0) → v
  29. LaTeX("\text{where \textcolor{#000099}{a ≠ 0}. The graph of any quadratic function is a parabola.}") → text21
  30. LaTeX((((("\text{the same power. In this case, although both terms contain the variable \textcolor{#000099}{x}, the first term, \textcolor{#000099}{" * mul1) * "x²}, has an exponent of \textcolor{#000099}{") * Multiplier) * "}.}")) → text17
  31. LaTeX((((((("\text{The expression to be multiplied is \textcolor{#000099}{(" * Multiplier) * "x)(") * Multiplicand) * "x -y)}. Notice that the first expression, \textcolor{#000099}{") * Multiplier) * "x}, only has one term.}")) → text3
  32. LaTeX((((("\text{\textcolor{#000099}{(" * Multiplier) * "x)(") * Multiplicand) * "x -y)}}")) → text6
  33. LaTeX((((((("\text{\textcolor{#000099}{= " * Multiplier) * "x\; •\; ") * Multiplicand) * "x + ") * Multiplier) * "x\; • -y}}")) → text8
  34. LaTeX((((("\text{\textcolor{#000099}{= " * mul1) * "x² + (-") * Multiplier) * "xy)}}")) → text10
  35. LaTeX((((("\text{\textcolor{#000099}{= " * mul1) * "x²-") * Multiplier) * "xy}}")) → text11
  36. LaTeX((((((((("\text{The result of applying the Distributive Property to \textcolor{#000099}{(" * Multiplier) * "x)(") * Multiplicand) * "x-y)} is \textcolor{#000099}{") * mul1) * "x² -") * Multiplier) * "xy}.}")) → text14
  37. LaTeX((((((((("\text{The result of multiplying \textcolor{#000099}{" * Multiplier) * "x} and \textcolor{#000099}{(") * Multiplicand) * "x-y)} is \textcolor{#000099}{ ") * mul1) * "x²-") * Multiplier) * "xy}. Recall that like terms must have the same variables raised to}")) → text16
  38. LaTeX((("\text{In the second term, \textcolor{#000099}{-" * Multiplier) * "xy}, the variable \textcolor{#000099}{x} has an understood exponent of \textcolor{#000099}{1}. Therefore, these terms are not like terms.}")) → text18
  39. LaTeX((((((((("\text{Thus, when \textcolor{#000099}{" * Multiplier) * "x} and \textcolor{#000099}{(") * Multiplicand) * "x-y)} are multiplied, the simplified result is \textcolor{#000099}{") * mul1) * "x² -") * Multiplier) * "xy}.}")) → text19
  40. LaTeX((((("\text{Find the product of \textcolor{#000099}{" * Multiplier) * "x\;}and\textcolor{#000099}{ \;(") * Multiplicand) * "x\; –\; y)}. Express the answer in simplest form.}")) → text1
  41. LaTeX("\text{\mathbf{quadratic \;function}}\text{ a function that can be written in the form \textcolor{#000099}{f(x) = ax² + bx + c},}") → text20
  42. LaTeX((("\text{Multiplier=" * Multiplier) * "x}")) → Datakit_Value1
  43. LaTeX((("\text{Multiplicand=(" * Multiplicand) * "x \textendash y)}")) → Datakit_Value2