Collecting Like Terms | 合并同类项

📚 Collecting Like Terms | 合并同类项

In IGCSE algebra, simplifying expressions is one of the first and most important skills you will master. The key step in almost every simplification is to collect like terms — that is, to group terms that have exactly the same variable part. This article explains the rules, common pitfalls and exam-style examples so that you can collect like terms quickly and accurately.

在 IGCSE 代数中，化简表达式是你首先要掌握也是最重要的技能之一。几乎每一次化简的关键步骤都是合并同类项——也就是说，把变量部分完全相同的项归为一组。本文讲解相关规则、常见错误和考试型例题，帮助你快速、准确地合并同类项。

1. What Are Terms and Like Terms? | 什么是项与同类项

An algebraic expression is made up of terms. A term is a number, a variable, or a product of numbers and variables. For example, 3x, −5, 2x² and 4xy are all terms.

代数表达式由项组成。项是一个数、一个变量，或数与变量的乘积。例如，3x、−5、2x² 和 4xy 都是项。

Like terms are terms that contain exactly the same variable or variables, each raised to the same power. The coefficients do not need to be the same. For instance, 3x and 5x are like terms, and −2x² and 7x² are like terms.

同类项是指含有完全相同的变量，且每个变量的指数也相同的项。系数不必相同。例如，3x 和 5x 是同类项，−2x² 和 7x² 也是同类项。

Terms such as 3x and 3x² are not like terms, because the powers of x are different. Similarly, 4xy and 4x are not like terms because one contains y and the other does not.

像 3x 和 3x² 这样的项不是同类项，因为 x 的指数不同。同样，4xy

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