📚 Collecting Like Terms | 合并同类项
In IGCSE Mathematics, collecting like terms is one of the first algebra skills you must master. It allows you to simplify expressions, solve linear equations, and prepare for higher topics such as expanding brackets and factorising.
在 IGCSE 数学中，合并同类项是你必须掌握的首批代数技能之一。它能帮助你简化表达式、解一元方程，并为进一步学习去括号和因式分解等内容打基础。
1. What Are Like Terms? | 什么是同类项
Like terms are terms in an algebraic expression that have exactly the same variable part. The variable part must include the same letters, and each letter must have the same exponent.
同类项是代数表达式中变量部分完全相同的项。变量部分必须含有相同的字母，并且每个字母的指数也必须相同。
For example, 3x and -5x are like terms because both have the variable x to the power 1. Similarly, 4xy and 2xy are like terms, and 7x² and -3x² are like terms.
例如，3x 和 -5x 是同类项，因为两者都含有一次变量 x。同样，4xy 和 2xy 是同类项，7x² 和 -3x² 也是同类项。
| Pair | Like? | Reason |
|---|---|---|
| 3x, -5x | Yes | Both have x¹ |
| 4xy, 2xy | Yes | Same variables x and y |
| 7x², -3x² | Yes | Same variable and same exponent 2 |
| 2x, 2y | No | Different letters |
| 3x, 3x² | No | Different exponents |
However, 2x and 2y are not like terms because the letters are different. Also, 3x and 3x² are not like terms because the exponent of x is different.
然而，2x 和 2y 不是同类项，因为字母不同；3x 和 3x² 也不是同类项，因为 x 的指数不同。
2. The Golden Rule of Collecting | 合并的黄金法则
The golden rule is simple: you can only add or subtract terms when their variable parts match exactly. If the variable part is not identical, the terms cannot be combined into a single term.
黄金法则很简单：只有当变量部分完全相同时，才能进行加减合并。如果变量部分不相同，就不能合并成一个单项。
For instance, 5a + 3a can become 8a, but 5a + 3b must be left as 5a + 3b. The expression is simplified, but the unlike terms remain separate.
例如，5a + 3a 可以合并为 8a，但 5a + 3b 必须保持为 5a + 3b。表达式已经简化，但不同类项仍需分开书写。
Remember that addition and subtraction are only possible for quantities of the same kind. In algebra, the variable part tells you the kind of quantity each term represents.
请记住，加法与减法只能对同类型的量进行。在代数中，变量部分说明了每一项所代表的数量类型。
3. Identifying Like Terms in an Expression | 在表达式中识别同类项
Begin by writing out each term together with its sign. A term is separated by a plus or minus sign. Then group terms that share the same variable part.
首先把每一项连同其前面的符号写出来。项由加号或减号分隔。然后将具有相同变量部分的项归为一组。
Consider the expression 5a + 3b – 2a + 7b. The terms are 5a, 3b, -2a and 7b. The like pairs are 5a and -2a, and 3b and 7b.
考虑表达式 5a + 3b – 2a + 7b。它的项为 5a、3b、-2a 和 7b。同类项为
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