📚 Collecting Like Terms | 合并同类项
In algebra, expressions often contain several similar parts that can be simplified. Collecting like terms is the process of adding or subtracting terms that have exactly the same variable and power. It is one of the most important basic skills in IGCSE Mathematics because it makes expressions shorter and helps you solve equations, factorise, and rearrange formulae.
在代数中，表达式常常包含几个可以简化的相似部分。合并同类项就是把变量和次数完全相同的项相加或相减的过程。这是 IGCSE 数学中最重要的基本技能之一，因为它能让表达式更短，并帮助你解方程、因式分解和变换公式。
1. What Is a Term? | 什么是项
A term is a single number, a single variable, or a product of numbers and variables. In the expression 4x² + 3x − 7, the terms are 4x², 3x and −7. Terms are separated by + or − signs.
项是指一个单独的数、一个单独的变量，或者数与变量的乘积。在表达式 4x² + 3x − 7 中，各项分别是 4x²、3x 和 −7。项与项之间用 + 或 − 号分隔。
Each term has a coefficient and a variable part. For example, in 5xy, the coefficient is 5 and the variable part is xy. The coefficient tells you how many of that variable part you have.
每个项都有一个系数和一个变量部分。例如，在 5xy 中，系数是 5，变量部分是 xy。系数告诉你这个变量部分有多少个。
Term = coefficient × variable part
2. Like Terms and Unlike Terms | 同类项与不同类项
Like terms are terms that have exactly the same variable part, including the same power. For example, 3x and 5x are like terms because both contain x. However, 3x² and 5x are not like terms because the powers of x are different.
同类项是指变量部分完全相同的项，包括相同的次数。例如，3x 和 5x 是同类项，因为都含有 x。然而，3x² 和 5x 不是同类项，因为 x 的次数不同。
Unlike terms cannot be combined by simple addition or subtraction. You can only collect like terms.
不同类项不能通过简单的加法或减法合并。你只能合并同类项。
| Expression | Like or unlike? | Explanation |
| 3x and 7x | Like | Both have x to the power 1. |
| 3x and 3y | Unlike | Variables are different. |
| 2x² and 5x² | Like | Both have x². |
| 4xy and 4x | Unlike | One has xy, the other has x only. |
3. The Rule for Collecting Like Terms | 合并同类项的规则
To collect like terms, add or subtract the coefficients while keeping the variable part unchanged. For example, 2x + 6x means you have 2 lots of x plus 6 lots of x, giving 8 lots of x.
合并同类项时，将系数相加或相减，变量部分保持不变。例如，2x + 6x 表示你有 2 个 x 加上 6 个 x，得到 8 个 x。
ion is repeated addition. You can think of x as an object: 2 apples + 6 apples = 8 apples.
这个法则成立是因为乘法是重复加法。你可以把 x 想成一种物品：2 个苹果 + 6 个苹果 = 8 个苹果。
ax + bx = (a + b)x
4. Collecting Positive Terms | 合并正项
+ 3x, first collect the x terms: 2x + 3x = 5x, then write the y term separately: 5x + 4y.
从只含
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