📚 Collecting Like Terms | 合并同类项
Algebra can look complicated, but simplifying an expression is often just a matter of grouping and combining the same types of terms. In IGCSE mathematics, collecting like terms is a core skill that appears in equations, formulae, sequences and problem-solving questions.
代数看起来可能很复杂，但化简表达式往往只是把同类型的项分组并合并。在 IGCSE 数学中，合并同类项是一项核心技能，广泛出现在方程、公式、数列和应用题中。
1. What Are Like Terms? | 什么是同类项
Like terms are terms that contain exactly the same variable letters raised to exactly the same powers. The numbers in front, called coefficients, can be different. For example, 3x and -5x are like terms because both contain x raised to the power 1.
同类项是指含有完全相同的字母且各字母的指数也完全相同的项。字母前面的数叫做系数，系数可以不同。例如，3x 和 -5x 是同类项，因为它们都含有指数为 1 的 x。
3x and -5x are like terms.
3x 和 -5x 是同类项。
Unlike terms have different variable parts. For instance, 3x and 3x² are not like terms, because the powers of x are different. Similarly, 2xy and 2x are not like terms because one contains y and the other does not.
异类项则含有不同的字母部分。例如，3x 和 3x² 不是同类项，因为 x 的指数不同。同样，2xy 和 2x 也不是同类项，因为一个含 y，另一个不含。
The idea of like terms is the foundation of simplifying algebraic expressions. Once you can spot them quickly, collecting terms becomes automatic.
同类项的概念是化简代数表达式的基石。一旦你能快速识别它们，合并项就会变得自然流畅。
2. Identifying Like and Unlike Terms | 识别同类项与异类项
To decide whether two terms are like terms, compare the variable part only. The order of letters does not matter, so 2ab and -3ba are like terms. However, changing a power or adding a new letter makes the terms unlike.
判断两项是否为同类项时，只比较字母部分。字母顺序不影响判断，所以 2ab 和 -3ba 是同类项。但如果指数改变或增加了新的字母，它们就不再是同类项。
| Terms | Like or Unlike |
|---|---|
| 5m and -2m | Like |
| 4xy and 7yx | Like |
| 3x and 3x² | Unlike |
| 6p and 6q | Unlike |
The table shows that the coefficient is irrelevant when identifying like terms. Only the letters and their powers matter.
上表说明，识别同类项时系数无关紧要，只有字母及其指数才重要。
In longer expressions, it is useful to underline or circle each family of like terms with a different mark. This makes the grouping step much clearer.
在较长表达式中，用不同的标记给每组同类项画线或画圈会很有帮助。这样分组步骤会清晰得多。
3. The Basic Rule: Add or Subtract Coefficients | 基本规则：系数相加或相减
When you collect like terms, keep the variable part exactly the same and add or subtract the coefficients. For positive coefficients, the result is straightforward.
合并同类项时，字母部分保持不变，只把系数相加或相减。对于正系数，结果很直接。
4a + 7a = (4 + 7)a = 11a
For subtraction, subtract the coefficient only.
做减法时，只减去系数。
9m - 4m = (9 -
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