Collecting Like Terms | 合并同类项

📚 Collecting Like Terms | 合并同类项

In algebra, many expressions look complicated, but most of them can be made much simpler by collecting like terms. This topic is one of the most important foundation skills in IGCSE Mathematics because it is used in solving equations, plotting graphs, handling formulas, and answering word problems.

在代数中，许多表达式看起来很复杂，但大多数都可以通过合并同类项来化简。这是 IGCSE 数学中最重要的基础技能之一，因为它广泛应用于解方程、绘制图像、处理公式以及解答应用题。

This article explains what like terms are, how to collect them correctly, and how to avoid common mistakes in exams.

本文将解释什么是同类项、如何正确合并同类项，以及如何在考试中避免常见错误。

1. What Are Algebraic Terms? | 什么是代数项

In algebra, a term is a single number, a letter, or a product of numbers and letters. Terms are separated by addition or subtraction signs.

在代数中，项是单个数字、单个字母或数字与字母的乘积。项之间由加号或减号分隔。

For example, in the expression 5x + 2y − 3, the three terms are 5x, 2y, and −3.

例如，在表达式 5x + 2y − 3 中，三项分别是 5x、2y 和 −3。

The number part of a term is called the coefficient, and the letter part is called the variable part. In 5x, the coefficient is 5 and the variable part is x.

项中的数字部分称为系数，字母部分称为变量部分。在 5x 中，系数是 5，变量部分是 x。

A term with no letter, such as −3, is called a constant term.

不含字母的项，例如 −3，称为常数项。

2. Recognising Like Terms | 识别同类项

Like terms have exactly the same variable part, including the same letters and the same powers. Only the coefficients may be different.

同类项具有完全相同的变量部分，包括相同的字母和相同的幂次，只有系数可以不同。

For example, 4x and −7x are like terms, while 3x and 3x² are not like terms because the powers of x are different.

例如，4x 和 −7x 是同类项，而 3x 和 3x² 不是同类项，因为 x 的幂次不同。