Collecting Like Terms | 合并同类项

📚 Collecting Like Terms | 合并同类项

In algebra, simplifying expressions is one of the most important skills you will need for IGCSE. The process of “collecting like terms” allows us to combine terms that have the same variable parts, making expressions shorter and easier to work with.

在代数中，化简表达式是 IGCSE 考试最重要的技能之一。”合并同类项” 的过程让我们把具有相同变量部分的项合并起来，使表达式更简短、更易于处理。

1. What Are Terms? | 什么是”项”？

A term is a number, a variable, or a product of numbers and variables. For example, 3x, -5y², 2xy and 7 are all terms. In 3x, the number 3 is called the coefficient and x is the variable part.

项是一个数、一个变量，或数与变量的乘积。例如：3x、-5y²、2xy 和 7 都是项。在 3x 中，数字 3 称为系数，x 是变量部分。

A constant term, such as 7 or -2, has no variable attached. Every term carries its own sign: in 4x – 3y + 2, the signs are +4x, -3y, and +2.

常数项如 7 或 -2 不包含变量。每个项都带有自己的符号：在 4x – 3y + 2 中，各项符号分别为 +4x、-3y 和 +2。

term = coefficient × variable part

2. Like Terms vs Unlike Terms | 同类项与非同类项

Like terms have exactly the same variable part, including the same powers. For example, 3x and 5x are like; 4x² and -2x² are like; 2xy and 3yx are also like because xy = yx.

同类项必须具有完全相同的变量部分，包括相同的指数。例如：3x 和 5x 是同类项；4x² 和 -2x² 是同类项；2xy 和 3yx 也是同类项，因为 xy = yx。

Terms such as 3x and 3x² are not like terms, because the powers of x are different. Likewise, 2x and 2y are not like, because the variables are different.

3x 和 3x² 不是同类项，因为 x 的指数不同；同样，2x 和 2y 也不是同类项，因为变量不同。