5是代数表达式吗？

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，代数方程过去写成“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。

5是代数表达式吗？

回答：

As it is clearly seen that 5 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 5 is not an algebraic expression.

示例问题

问题1：从下列代数表达式中找出常数，

• x ³ + 2x ² – 9
• 10 + 年⁵

回答：

Constants are the terms that do not have any variable attached to them, therefore, in the first case, -9 is the constant, and in the second case 10 is the constant.

问题 2：找出以下表达式中存在的项数，

• 2x ² + 5x – 5
• 是⁷ – 133

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：简化代数项，3z ⁵ + z ³ – y ⁶ + 7z ⁵ – 6y ⁶ + 56 + 11z ³ + 10

解决方案：

In the expression, there are terms with the same power and same variable that are repeated, first bring them together,

(3z⁵ + 7z⁵) + (z³ + 11z3) – (y⁶ – 6y6) + 56 + 10.

Now, simplify the expression,

10z⁵ + 12z³ – 7y⁶ + 66.

问题4：99是代数表达式吗？

回答：

As it is clearly seen that 99 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 99 is not an algebraic expression.