📚 Collecting Like Terms | 合并同类项
In algebra, expressions often contain several terms. A term is a number, a variable, or a product of numbers and variables. Collecting like terms means simplifying an expression by adding or subtracting terms that have exactly the same variable part. This is one of the most important foundation skills in IGCSE mathematics.
在代数中，表达式通常包含多个项。项是一个数、一个变量，或者是数与变量的乘积。合并同类项是指通过加减具有完全相同变量部分的项来化简表达式。这是 IGCSE 数学中最重要的基本功之一。
1. What Are Like Terms? | 什么是同类项？
A term is built from a coefficient and a variable part. For example, in the term 3x, the coefficient is 3 and the variable part is x. In the term -5y², the coefficient is -5 and the variable part is y².
一个项由系数和变量部分组成。例如，在 3x 中，系数是 3，变量部分是 x；在 -5y² 中，系数是 -5，变量部分是 y²。
Like terms are terms that have the same variables raised to the same powers. For example, 3x and -2x are like terms because both contain x. The numbers 4 and -7 are also like terms because they are both constant terms.
同类项是指所含变量相同且对应指数也相同的项。例如，3x 和 -2x 是同类项，因为它们都含有 x；4 和 -7 也是同类项，因为它们都是常数项。
Here are some examples of like and unlike terms:
下面是一些同类项与不同类项的例子：
| Like terms 同类项 | Unlike terms 不同类项 |
| 5x and 2x | 5x and 2x² |
| 3y² and -y² | 3y² and -3y |
| 7 and -2 | 7 and -2x |
| 4ab and -ab | 4ab and 4a |
2. Why Do We Collect Like Terms? | 为什么要合并同类项？
Collecting like terms makes an expression shorter and easier to understand. Instead of writing 5x + 3x, we can write 8x. This helps us evaluate the expression quickly and avoid errors in longer problems.
合并同类项能让表达式更简短、更容易理解。把 5x + 3x 写成 8x，既节省时间，也能避免在较复杂的问题中出错。
We also collect like terms when solving equations. Rearranging and simplifying both sides of an equation is an essential step before isolating the variable. For example, 4x + 2x – 5 = 19 becomes 6x – 5 =
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