什么是没有变量的术语?
代数表达式始于 9 世纪。一开始,它更多的是陈述形式,根本不是数学形式。例如,代数方程曾经写成“5 乘以 3 得到 18”,基本上是 5x + 3 = 18。这种不是数学的方程就是巴比伦代数。代数随着时间和提供的不同形式而发展。它从埃及代数开始,然后是巴比伦代数,然后是希腊几何代数,然后是丢番图代数,然后是印度代数,然后是阿拉伯代数,最后是抽象代数。今天,为了更好地理解,最简单、最方便的代数形式在课堂上教授。
代数表达式
代数表达式是由变量、常数和数学运算(如加法、减法、乘法、除法等)组合而成的表达式。代数表达式由多项组成,方程中可以有一项或多项。让我们了解代数表达式中使用的基本术语,
常数、变量、系数和项
在代数表达式中,固定数值称为常数,常数不附加任何变量。例如,3x – 1 有一个常数 -1。变量是代数表达式中存在的未知值,例如,4y + 5z 将 y 和 z 作为变量。系数是附加到变量的固定值(实数),它们与变量相乘。例如, 5x 2 + 3 有 5 作为 x 2的系数。项可以是常数、变量或两者的组合,基本上,每个项由加法或减法分隔。例如,3x + 5、3x 和 5 是术语。
什么是没有变量的术语?
回答:
A term can be a constant, a variable, or a combination of both. It is known that if the term does not have any variable, it will have only a constant. Therefore, it can be concluded that a term without a variable is a constant. For example, if a term is 5x, x is the variable, and 5 is the constant. Therefore, if x is removed from 5x, only 5 is remaining. Hence, only constant remains.
示例问题
问题1:从下列代数表达式中找出常数,
- 4x 3 + 2x 2 – 9x + 3
- 13 + 年5
回答:
Constants are the terms that do not have any variable attached to them, therefore, in the first case, +3 is the constant, and in the second case, 13 is the constant.
问题 2:找出以下表达式中存在的项数,
- 7x 2 + 4x – 10
- 3 年7 – 45
回答:
Terms are separated by each other either by addition or subtraction sign. Therefore, in the first case, there are 3 terms and in the second case, there are 2 terms.
问题 3:12 是代数表达式吗?
回答:
As it is clearly seen that 12 is a constant, even though, constants are a part of the algebraic expression, they do not complete the algebraic expression. For an expression to be an algebraic expression, a variable, and an operator is required as well. Variable can be any unknown term, for instance, x, y, z, etc. and, the operator can be +, -. Therefore, it is concluded that 12 is not an algebraic expression.