12.1 承认和识别单质、二族和三族

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  识别和识别单质、二族和三族

  

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  Sam saw this expression in his math book.
  ::Sam在数学书里看到了这个表情

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  $\begin{array}{r}{x}^2-8\end{array}$
  ::x2-8

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  He isn’t sure how to classify this expression. Do you know?
  ::他不知道该如何分类这个表达方式。

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  In this concept, you will learn to recognize and identify monomials, binomials and trinomials.
  ::在这个概念中,你将学会认识和识别单一的、二元的和三元的。

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  Monomials and Polynomials
  ::单体和多面体

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  Sometimes, an expression or an equation will have exponents and variables in it. These expressions and equations can have more than one variable and sometimes more than one exponent . To understand how to work with these variables and exponents, you have to understand . A polynomial is an algebraic expression that shows the sum of monomials.
  ::有时,一个表达式或一个方程式会包含引言和变量。这些表达式和方程式可以包含多个变量,有时可以包含多个示例。要理解如何与这些变量和引言一起工作,您必须理解。多义是一个代数表达式,显示单数的总和。

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  A monomial is an expression in which variables and constants may stand alone or be multiplied. A monomial cannot have a variable in the denominator. You can think of a monomial as being one term .
  ::单数表达式是变量和常数可以单独存在或乘以的表达式。单数不能在分母中存在变量。您可以将单数视为一个术语。

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  To understand these new terms better, let’s look at some word prefixes. The chart below shows some common terms and the meaning of their prefixes.
  ::为了更好地理解这些新术语,让我们看看一些字前缀。 下面的图表显示了一些共同术语及其前缀的含义。

  

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  In math these prefixes are used often. Each prefix will give a hint as to the type of expression that you are dealing with. The prefix mono, for example, means one, a monomial is a single piece or term.
  ::在数学中经常使用这些前缀。 每个前缀将提示您正在处理的表达式类型。 前缀单词, 例如, 意指一个, 单面条是一个或一个术语 。

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  Here are some monomials:
  ::以下是一些单项协议:

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  $\begin{array}{r}5x^3-2x^5{x}^{2}y\end{array}$
  ::5x3-2x5x2y

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  The prefix poly means many. So the word polynomial refers to one or more than one term in an expression. The relationship between these terms may be sums or difference .
  ::前缀组合有许多含义。 因此, 多式单词在表达式中指一个或多个词。 这些词之间的关系可以是总和,也可以是差数。

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  Here are some polynomials:
  ::以下是多面性:

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  $\begin{array}{r}{x}^2+52x-8+4x^5-7a^2+9b-4b^3+6\end{array}$
  ::x2+52x-8+4x5-7a2+9b-4b3+6

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  You call an expression with a single term a monomial, an expression with two terms is a binomial , and an expression with three terms is a trinomial . An expression with more than three terms is named simply by its number of terms. For example a polynomial with five terms is called a five-term polynomial.
  ::您将单一术语表达法称为单一术语,将两个术语表达法称为二进制术语,将三个术语表达法称为三进制术语。使用三个以上术语的表达法仅按其术语编号命名。例如,使用五个术语的多进制术语被称为五进制多进制术语。

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  From the information above, you can name the expressions as follows:

  

  
  ::从以上信息中,您可以命名表达式如下:

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about  Sam. Sam has the expression $\begin{array}{r}{x}^2-8\end{array}$  and needs to classify it.
  ::早些时候,你曾遇到关于Sam的问题。Sam有 x2-8 的表达方式,需要分类。

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  First, count the number of terms. In this expression there are two terms.
  ::首先,计算术语数。在此表达式中有两个术语。

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  Next, classify the expression based on the number of terms. Two terms means it is a binomial.
  ::接下来,根据术语数对表达式进行分类。两个词表示它是二进制表达式。

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  The answer is binomial.
  ::答案是二元论。

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  Example 2
  ::例2

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  How would you identify the following expression? 
  ::您将如何识别以下表达式 ?

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  $\begin{array}{r}4x^2-8y+4\end{array}$
  ::4x2-8y+4

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  First, consider how many terms are in the expression.
  ::首先,考虑这个用语中有多少个术语。

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  This expression has three terms.
  ::这个表达方式有三个词。

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  Therefore , this expression is called a trinomial.
  ::因此,这一表述被称为三审。

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  Example 3
  ::例3

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  Identify the expression $\begin{array}{r}4x^3-8\end{array}$ .
  ::识别4x3-8表达式。

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  First, consider how many terms are in the expression.
  ::首先,考虑这个用语中有多少个术语。

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  This expression has two terms.
  ::这个表达方式有两个词。

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  The answer is binomial.
  ::答案是二元论。

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  Example 4
  ::例4

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  Identify the expression $\begin{array}{r}{x}^2+3x+9\end{array}$ .
  ::标识表达式 x2+3x+9 。

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  First, consider how many terms are in the expression.
  ::首先,考虑这个用语中有多少个术语。

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  This expression has three terms.
  ::这个表达方式有三个词。

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  The answer is trinomial.
  ::答案是三元论。

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  Example 5
  ::例5

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  Identify the expression $\begin{array}{r}6xy\end{array}$ .
  ::标识表达式 6xy 。

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  First, consider how many terms are in the expression.
  ::首先,考虑这个用语中有多少个术语。

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  This expression has one term.
  ::此表达式有一个术语 。

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  The answer is monomial.
  ::答案是单一的。

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  Review
  ::回顾

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  Use the chart to identify each term with the correct label.
  ::使用图表用正确的标签来识别每个术语。

  Number of Terms	1	2	3	4
  Name	monomial	binomial	trinomial	four-term polynomial
  Expression	$\begin{array}{r}-2x^5\end{array}$	$\begin{array}{r}{x}^2+5\end{array}$	$\begin{array}{r}3x-8+4x^5\end{array}$	$\begin{array}{r}-7a^2+9b-4b^3+6\end{array}$

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  1.  $\begin{array}{r}4x^2\end{array}$
  ::1. 4x2

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  2.  $\begin{array}{r}3x+7\end{array}$
  ::2. 3x+7

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  3.  $\begin{array}{r}9x^2+6y\end{array}$
  ::3. 9x2+6y

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  4.  $\begin{array}{r}{x}^2+2y^2+8\end{array}$
  ::4. x2+2y2+8

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  5.  $\begin{array}{r}5c^3\end{array}$
  ::5. 5c3

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  6.  $\begin{array}{r}3x^2+4x+3y^2+7\end{array}$
  ::6. 3x2+4x+3y2+7

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  7.  $\begin{array}{r}4x+3xy+9\end{array}$
  ::7. 4x+3xy+9

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  8.  $\begin{array}{r}2x^2+7y+9\end{array}$
  ::8. 2x2+7y+9

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  9.  $\begin{array}{r}14xy\end{array}$
  ::9. 14xy

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  10.  $\begin{array}{r}4x^2+5x-9\end{array}$
  ::10. 4x2+5x-9

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  11.  $\begin{array}{r}5x^3-4x^2+3x-10\end{array}$
  ::11. 5x3-4x2+3x-10

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  12.  $\begin{array}{r}4x\end{array}$
  ::12. 4x

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  13.  $\begin{array}{r}16x+4\end{array}$
  ::13. 16x+4

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  14.  $\begin{array}{r}18x^2+5x-8\end{array}$
  ::14. 18x2+5x-8

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  15.  $\begin{array}{r}9xyz\end{array}$
  ::15. 9xyz

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  16.  $\begin{array}{r}5xy-6x\end{array}$
  ::16. 5xy-6x

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  17.  $\begin{array}{r}18x^2-9x\end{array}$
  ::17. 18x2-9x

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  Review (Answers)
  ::回顾(答复)

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  Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

   

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  Resources
  ::资源