📚 Collecting Like Terms | 合并同类项
In IGCSE mathematics, algebra often asks you to simplify expressions by 'collecting like terms'. This skill is the foundation for solving equations, expanding brackets, and working with formulas. A like term is a term that has exactly the same variable part, including the same letters and the same powers.
在 IGCSE 数学中，代数经常要求你通过“合并同类项”来化简表达式。这项技能是解方程、去括号和使用公式的基础。同类项是指变量部分完全相同的项，包括相同的字母和相同的指数。
1. What Are Like Terms? | 什么是同类项
A term is a single number, a variable, or a product of numbers and variables. For example, in 3x + 5y - 7, the terms are 3x, 5y, and -7.
项是一个单独的数、一个变量，或数与变量的乘积。例如，在 3x + 5y - 7 中，项是 3x、5y 和 -7。
Like terms have exactly the same variable factors. 4x and 9x are like terms, but 4x and 4x² are not like terms because the powers of x are different.
同类项有完全相同的变量因式。4x 和 9x 是同类项，但 4x 和 4x² 不是同类项，因为 x 的指数不同。
The coefficient, the number in front of the variable, can be different. When we collect like terms, we add or subtract the coefficients and keep the variable part unchanged.
系数，即变量前面的数，可以不同。合并同类项时，我们只对系数进行加减，变量部分保持不变。
2. Identifying Like Terms | 识别同类项
To identify like terms, ignore the coefficient and focus on the variable letters and their exponents. For instance, 2ab and -7ab are like, while 2ab and 3a²b are unlike.
要识别同类项，先忽略系数，只看变量字母及其指数。例如，2ab 和 -7ab 是同类项，而 2ab 和 3a²b 不是。
A quick check is to cover the number in front and ask: are the remaining variable parts identical? If yes, the terms can be collected.
一个快速检查方法是遮住前面的数字，问自己：剩下的变量部分是否完全相同？如果是，这些项就可以合并。
For example, 2x and 5x are like, 3x² and 7x² are like, 4xy and -xy are like, and all constants such as 6 and -2 are like terms.
例如，2x 和 5x 是同类项，3x² 和 7x² 是同类项，4xy 和 -xy 是同类项，而所有常数项如 6 和 -2 也是同类项。
By contrast, 5x and 5y are unlike because the variables are different. Likewise, 4x and 4x² are unlike because the powers of x are different.
相比之下，5x 和 5y 不是同类项，因为变量不同。同样，4x 和 4x² 也不是同类项，因为 x 的指数不同。
3. Why Collecting Like Terms Matters | 为什么合并同类项很重要
Collecting like terms makes algebra shorter and clearer. Instead of writing x + x + x + 2x, you can write 5x.
合并同类项使代数表达式更简洁、更清晰。比如不用写 x + x + x + 2x，你可以写成 5x。
. An equation such as 3x + 2 + 5x - 7 = 0 must be simplified to 8x - 5 = 0 before solving.
这也是解方程前必不可少的步骤。比如方程 3x + 2 + 5x - 7 = 0 必须先化简为 8x - 5 = 0 才能求解。
Many IGCSE questions reward the simplification step, even if the final answer has a small arithmetic error. Clear working is therefore very important.
许多 IGCSE 题目会给化简步骤分，即使最后答案有一点算术错误。因此，清晰的过程非常重要。
4. Adding and Subtracting Like Terms | 同类项的加减合并
lect like terms, add or subtract their coefficients. For example, 5a + 3a = (5 + 3)a = 8a.
合并同类项时，把系数相加或相减。例如，5a + 3a = (5 + 3)a = 8a。
5a + 3a = 8a
For subtraction, be careful with negative signs. 9p - 2p - 4p = (9 - 2 - 4)p = 3p.
做减法时要小心负号。9p - 2p - 4p = (9 - 2 - 4)p = 3p。
ent is not written, it is 1. For example, x + x + x = 3x because each x has coefficient 1.
如果没有写出系数，系数就是 1。例如，x + x + x = 3x，因为每个 x 的系数都是 1。
Always keep the variable and its power exactly the same. 7n² + 2n² = 9n², not 9n⁴.
始终保持变量及其指数完全相同。7n² + 2n² = 9n²，而不是 9n⁴。
5. Combining Single-Variable Terms | 合并单变量项
Start by grouping all terms that contain the same variable. In 6x + 3 - 2x + 8, group 6x and -2x, then group 3 and 8.
首先把所有包含相同变量的项放在
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