摘要:乘数代数表达式

In this chapter, we learned about:
::在本章中,我们了解到:

Recognizing Expressions That Can Be Factored 
::承认可以考虑的表达方式

播放段落
• To recognize a greatest common factor, find a greatest common factor for the numbers in the expression and then consider each variable or expression separately. If the variable or expression appears in all of the terms, factor out the smallest power that appears.
  ::要识别一个最大的共同因素, 找到表达式中数字的最大共同因素, 然后分别考虑每个变量或表达式。 如果变量或表达式在所有术语中都出现, 请将显示的最小功率考虑在内 。
播放段落
• To recognize a perfect square trinomial, the first and the last terms must be perfect squares. The middle term must two times the square roots of each of the perfect squares.
  ::为了承认一个完美的平方三角,第一个和最后一个条件必须是完美的平方。 中期必须是每个完美的平方的平方根的两倍。
播放段落
• To recognize a difference of two squares, the two terms need to be perfect squares and the operation between them needs to be subtraction.
  ::要承认两个方形的差别,这两个词必须是完美的方形,它们之间的操作需要减去。
播放段落
• To recognize an expression that is quadratic in form, the variable part of one term needs to be the square of the variable part in another term.
  ::要承认形式上为二次形的表达式,一个术语的可变部分必须是另一个术语中可变部分的正方形。

Factoring
::保理

播放段落
• To factor out a GCF, write the GCF outside of the parentheses and divide each one of the terms by the GCF in the parentheses.
  ::将绿色气候基金考虑在内,在括号外填写绿色气候基金,在括号内按绿色气候基金分列每个用语。
播放段落
• To factor a perfect square trinomial, we have two forms either $\begin{array}{r}(a+b{)}^2=a^2+2ab+b^2\end{array}$  or $\begin{array}{r}(a-b{)}^2=a^2-2ab+b^2\end{array}$ .  
  ::要计算一个完美的平方三角,我们有两种形式,要么是(a+b)2=a2+2ab+b2,要么是(a-b)2=a2-2ab+b2。
播放段落
• To factor a difference of two squares, we use the form $\begin{array}{r}{a}^2-b^2=(a+b)(a-b)\end{array}$ .
  ::乘以两个方形的差,我们使用表A2-b2=(a+b)(a-b)-b。
播放段落
• To factor a sum of cubes, we have the form: $\begin{array}{r}{a}^3+b^3=(a+b)(a^2-ab+b^2)\end{array}$ .
  ::乘以立方体的总和,我们有窗体:a3+b3=(a+b)(a2-ab+b2)。
播放段落
• To factor a difference of cubes, we have the form: $\begin{array}{r}{a}^3-b^3=(a-b)(a^2+ab+b^2)\end{array}$ .
  ::乘以差异的立方体,我们有表单:a3-b3=(a-b)(a2+ab+b2)。
播放段落
• To factor quadratic expressions of the form $\begin{array}{r}a{x}^2+bx+c\end{array}$  where $\begin{array}{r}a=1\end{array}$ , you need to find a pair of numbers whose product is c and whose sum is b .
  ::在 a=1 的情况下,您需要找到产品为 c 且其总和为 b 的一对数字来表示窗体 ax2+bx+c 的二次形表达式。
播放段落
• To factor quadratic expressions of the form $\begin{array}{r}a{x}^2+bx+c\end{array}$  when $\begin{array}{r}a\ne 1\end{array}$ , you need two numbers whose product is ac and whose sum is b . Then, you can separate the bx -term using those two numbers and factor by grouping.
  ::当 a\\\ 1 时, 您需要两个数字, 其产品为 ac, 其总和为 b. 时, 乘以窗体 ax2+bx+c 的二次表达式。 然后, 您可以使用这两个数字和因数分组, 将 bx- 期分开 。
播放段落
• Alternately, you can divide each of the numbers by a and put them as the second term in a binomial. At least one will have a denominator, which becomes the leading coefficient of the binomial.
  ::或者,你可以将每个数字除以一个,然后把它们作为二进制的第二学期。 至少一个数字将有一个分母,它将成为二进制的主要系数。
播放段落
• To factor by grouping, look for terms that have a GCF and factor the GCF out of those terms. If you can factor by grouping, what remains after you factor will also be a GCF and you can factor that out to factor completely.
  ::通过分组,寻找具有全球合作框架的术语,并将全球合作框架从这些术语中扣除。如果能够通过分组来计算,那么在你们之后的因素也将是全球合作框架,并且可以将因素完全考虑在内。
播放段落
• To factor an expression that is quadratic in form, use a dummy variable to rewrite the expression as a quadratic expression, factor the expression, and then replace the dummy variable at the end of the process.
  ::将表达式乘以形式为二次形的表达式,使用假变量将表达式重写为二次形表达式,乘以表达式,然后在进程结束时替换假变量。

Looking Back, Looking Forward
::回顾,展望未来

In this chapter, we learned how to factor expressions. We will use this in Chapter 9 for all of the applications we use factoring of numbers for: finding a least common multiple to add and subtract algebraic fractions, and simplifying algebraic fractions. Factoring will help us solve equations in many of the chapters that follow, including quadratic and higher-degree polynomial equations, rational equations, and even some equations that involve radicals and exponents that are variables. Writing a function in factored form will be essential for finding the x -intercepts of the function, which has several applications. Factoring is an essential skill for an algebra student and will be used extensively going forward.   
::在本章中,我们学会了要素表达式。我们将在第9章中用这个来应用数字的系数,以便:找到一个最不常见的倍数来增减代数分数,简化代数分数。计算法将帮助我们解决随后许多章节中的方程,包括四度和更高度多角度方程、理性方程,甚至一些涉及激进和引言的公式,它们是变量。以系数形式写入一个函数对于找到函数的 X inter 至关重要,因为函数的 X inter 有几个应用程序。计算法是升数学生的基本技能,并将被广泛使用。

Chapter Review
::回顾章次审查