5x 和 4xy 是类似的术语吗？

代数的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。该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被定义为代数表达式。

什么是代数表达式？

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。

代数表达式的类型

根据表达式中项的数量，代数表达式分为 3 个部分：

• 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 5×4, 3xy, 2x, 5y, 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 2xy + 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.

32x + 15y is a polynomial of two terms in two variables x and y.

15ab + 55a + 25 is a polynomial of three terms in two variables a and b.

其他类型的表达

除了单项式、二项式和多项式类型的表达式之外，我们还有其他表达式

• 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 14 + 5, 18 ÷ 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 4x + y, 5ab + 53, etc.

一些重要的代数公式

有一些基本使用的代数表达式术语，

(a + b)² = a² + 2ab + b²

(a – b)² = a² – 2ab + b²

(a + b)(a – b) = a² – b²

(x + a)(x + b) = x² + x(a + b) + ab

(a + b)³ = a³ + b³ + 3ab(a + b)

(a – b)³ = a³ – b³ – 3ab(a – b)

a³ – b³ = (a – b)(a² + ab + b²)

a³ + b³ = (a + b)(a² – ab + b²)

示例：如果 2x ² +3xy+4x+7 是代数表达式。确定方程。

解决方案：

2x², 3xy, 4x, and 7 are the Terms

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

5x 和 4xy 是类似的术语吗？

回答：

Like terms: Terms that are having same variable or terms having variables with the same exponent power for them are called Like terms.

Example: 6x & 16x and 5xy² & 8xy², here, 6x and 16x are called Like Terms because they have the same coefficient of x .

Unlike terms: Terms that are having different variables or terms having variables with different exponent power for them are called Unlike terms.

Example: 7z & 16x and 7x² & 7x³, here, 7z and 16x are called Unlike Terms because they have different coefficients of z and x .

Now the answer to the above question is NO, 5x and 4xy are not like terms as 5x and 4xy both have different variables with different coefficient of x and y.

类似问题

问题 1：类似术语的示例？

回答：

Terms that are having same variable or terms having variables with the same exponent power for them are called Like terms.

Example : 4x, 6x, 9x, and -3x

Here x is the common variable in all the above terms so these are like terms.

问题 2：不同术语的示例？

回答：

Terms that are having different variables or terms having variables with different exponent power for them are called Unlike terms.

Example : 2x + 19y , 4x – 5x² , 5x + 6y 

问题 3：从以下内容中识别相似术语和不同术语：

8zy ² x, 2y ² z, 7xy ² z, 3xz ² y ² , 4x ² yz

回答：

Like Terms: 8zy²x,7xy²z

Now Unlike terms = 2y²z, 3xz²y², 4x²yz 

问题 4：3x + 5 是什么类型的代数表达式？

回答：

An algebraic expression which is having two terms and unlike are termed as a binomial expression.

Here 3x + 5 has two monomial 3x and 5 and hence it is a binomial and every binomial is a type of polynomial.  

Therefore, 3x + 5 is a binomial.