Collecting Like Terms | 合并同类项

📚 Collecting Like Terms | 合并同类项

In IGCSE algebra, collecting like terms is one of the first and most important skills for simplifying expressions. This guide explains how to recognise like terms, combine them correctly, and avoid the errors that frequently cost marks in exams.

在 IGCSE 代数中，合并同类项是化简表达式时最先学习也最重要的技能之一。本文将讲解如何识别同类项、正确合并它们，并避免考试中经常丢分的错误。

1. Terms, Coefficients and Variables | 项、系数与变量

An algebraic expression is built from terms. A term can be a single number, a letter, or a product of numbers and letters. Examples include 5x, −3y, 7x², 4xy, and 9. The number in front of the letters is called the coefficient. In 5x, the coefficient is 5; in −3y, the coefficient is −3.

代数表达式由项组成。项可以是一个数字、一个字母，也可以是数字和字母的乘积。例如 5x、−3y、7x²、4xy 和 9。字母前面的数字称为系数。在 5x 中，系数是 5；在 −3y 中，系数是 −3。

Variables are the unknown letters such as x, y, a, b or t. A constant term is a term with no variable, such as 4 or −7. Being able to separate the coefficient, variable part and exponent in each term makes collecting like terms much easier.

变量是表示未知数的字母，例如 x、y、a、b 或 t。常数项是没有字母的项，例如 4 或 −7。能够把每一项拆分为系数、字母部分和指数，会让合并同类项变得容易得多。

For the term 6x², the coefficient is 6, the variable is x, and the exponent is 2. For the term −4ab, the coefficient is −4, and the variable part is ab. Always include the sign as part of the coefficient.

对于 6x² 这一项，系数是 6，变量是 x，指数是 2。对于 −4ab 这一项，系数是 −4，字母部分是 ab。符号始终要算作系数的一部分。

2. What Makes Terms ‘Like’? | 什么是“同类项”？

Two or more terms are called like terms when they have exactly the same variable part and each variable has the same power. Coefficients can be different. For example, 3x and 7x are like terms because both contain x with power 1.

两个或多个项，如果它们的字母部分完全相同且每个字母的指数也相同，就称为同类项。系数可以不同。例如，3x 和 7x 是同类项，因为二者都含有 x 且 x 的指数为 1。

Unlike terms have different variable parts or different powers. For instance, 3x and 3y are not like terms because the variables differ. Also, 2x and 2x² are not like terms because the powers of x are different.

不同类项的字母部分或指数不同。例如，3x 和 3y 不是同类项，因为变量不同。同样，2x 和 2x² 也不是同类项，因为 x 的指数不同。