📚 Collecting Like Terms | 合并同类项
Welcome to this revision guide for G-2, Topic 15: Collecting Like Terms. This skill is one of the most important foundations in IGCSE Mathematics.
欢迎阅读 G-2 课本主题 15「合并同类项」复习指南。这是 IGCSE 数学中最重要的基础技能之一。
Collecting like terms means simplifying an algebraic expression by adding or subtracting terms that have exactly the same variable part.
合并同类项，就是把代数表达式中变量部分完全相同的项通过加法或减法合并，从而化简表达式。
1. What Are Like Terms? | 什么是同类项
In algebra, a term is a single number, a variable, or a product of numbers and variables. For example, 3x, -5y² and 7 are all terms.
在代数中，项是一个单独的数、一个变量，或数字与变量的乘积。例如，3x、-5y² 和 7 都是项。
Like terms are terms that have exactly the same variables, with the same powers. Their coefficients may be different.
同类项是指变量完全相同，且每个变量的次数也完全相同的项。同类项的系数可以不同。
3x and -9x are like terms because both contain x to the power 1.
3x 与 -9x 是同类项，因为它们都含有一次变量 x。
2x² and 5x² are like terms because both contain x².
2x² 与 5x² 是同类项，因为它们都含有 x²。
3x and 3x² are not like terms, because the powers of x are different.
3x 与 3x² 不是同类项，因为 x 的次数不同。
4xy and 2yx are like terms, because xy = yx by the commutative property.
4xy 与 2yx 是同类项，因为根据乘法交换律 xy = yx。
2. Why Do We Combine Like Terms? | 为什么要合并同类项
Combining like terms makes an expression shorter and easier to use. It also helps us solve equations later.
合并同类项能让表达式更简洁、更容易使用，也方便我们后续解方程。
ut 3 apples and 2 bananas cannot be counted as one type, just as 3x + 2y cannot be simplified.
如果你有 3 个苹果和 2 个苹果，你一共有 5 个苹果。同理，3x + 2x = 5x。但 3 个苹果和 2 根香蕉不能算作一种水果，所以 3x + 2y 不能合并。
For example, 5x + 2y - x can be simplified by combining 5x and -x to get 4x + 2y.
例如，5x + 2y - x 可以合并 5x 与 -x，得到 4x + 2y。
3. Identifying Like Terms | 识别同类项
To identify like terms, check two things: the variables must be the same, and the powers of those variables must be the same.
要识别同类项，需要检查两点：变量必须相同，并且这些变量的次数也必须相同。
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