代数表达式是如何形成的？

代数的基本概念教会了我们如何使用 x、y、z 等字母来表示未知值。这些字母在这里被称为变量。这个表达式可以是变量和常量的组合。任何放在变量之前并乘以变量的值都称为系数。

使用字母或字母表示数字而不指定其实际值的想法称为代数表达式。

什么是代数表达式？

在数学中，它是由变量和常数以及诸如加法、减法等代数运算组成的表达式。这些表达式由项组成。代数表达式是对任何变量进行加减乘除等运算时的方程。

A combination of terms by the operations such as addition, subtraction, multiplication, division, etc is termed as an algebraic expression (or) a variable expression.

Examples: 2x + 4y – 7,  3x – 10, etc.

上述表达式是在未知变量、常数和系数的帮助下表示的。这三个术语的组合称为表达式。与代数方程不同，它没有边或“等于”符号。

它的一些例子包括

• 2x + 2y – 5
• 4x – 20
• 3x + 2

代数表达式的类型

• 单项式
• 二项式
• 多项式表达式

单项式

只有一项的表达式称为单项式表达式。

Examples of monomial expressions include 4x⁴, 2xy, 2x, 8y, etc.

二项式

具有两项且不同的代数表达式称为二项式表达式

Examples of binomial include 4xy + 8, xyz + x², etc.

多项式表达式

具有多个非负整数指数的变量的表达式称为多项式表达式。

Examples of polynomial expression include ax + by + ca,  x³ + 5x + 3, etc.

一些其他类型的表达

除了单项式、二项式和多项式外，还有一些其他类型的表达式

• 数值表达式
• 变量表达式

数值表达式

仅由数字和运算组成但从不包含任何变量的表达式称为数字表达式。

Some of the examples of numeric expressions are 11 + 5, 14 ÷ 2, etc.

变量表达式

包含变量以及用于定义表达式的数字和操作的表达式称为变量表达式。

Some examples of a variable expression include 5x + y, 4ab + 33, etc.

一些代数公式

(a + b) = a² + 2ab + b²

(a – b) = a² – 2ab + b²

(a + b)(a – b) = a² – b²

(x + a)(x + b) = x² + x(a + b) + ab

代数表达式有一些基本用的术语

使用这些术语的示例

如果 2x ² +3xy+4x+7 是代数表达式。

然后，2x ² 、3xy、4x 和 7 是术语

Coefficient of Term: 2 is the coefficient of x²

Constant term: 7

Variables: here x, y are variables

Factors of a term: If 2xy is a term, then its factors are 2, x, and y.

Like and Unlike Terms: Example of like and unlike terms:  

• Like terms: 4x and 3x  
• Unlike terms: 2x and 4y

代数表达式是如何形成的？

回答：

An algebraic expression is formed from variables and constants using different operations.

It is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, etc.. these Expressions are made up of terms. Algebraic expressions are the equations when the operations such as addition, subtraction, multiplication, division, etc. are operated upon any variable.

A combination of terms by the operations such as addition, subtraction, multiplication, division, etc is termed as an algebraic expression (or) a variable expression.

Examples: 2x + 4y – 7,  3x – 10, 4x + 7, etc.

here 4x + 7 is a term

x is a variable whose value is unknown and which can take any value.

here 4 is known as the coefficient of x, as it is a constant value used with the variable term.

7 is the constant value term that has a definite value.

示例问题

问题 1：简化 4 – 3(x – 1)。

解决方案：

Here we have

4 – 3(x – 1)

= 4 – 3x +3

= 7 – 3x

= -3x + 7

问题2：从以下代数表达式中找出常数，

x ³ + 3x ² – 4

2 + y ⁵

回答：

Constants are the terms that do not have any variable,

therefore, in the first term -4 is the constant and in the second term 2 is the constant.

问题 3：识别代数表达式的各个组成部分：

6x + 3y – 4。

解决方案：

The algebraic expression is constituted by the following parts:  

6x and 3y, where 6 and 3 are coefficients and x and y are variables. -4 is the constant part of the expression.

问题 4：求解 x = 3：x ² – 4x + 5

解决方案：

x² – 4x + 5

Here we have

3² – (4 × 3) + 5

= 9 – 12 + 5

= 14 – 12

= 2