📚 Collecting Like Terms | 合并同类项
In algebra, letters stand for unknown or changing quantities. An expression such as 3x + 5y - 2x + 7 contains separate parts called terms. To make expressions shorter and easier to use, we combine the terms that have exactly the same variable part. This skill is called collecting like terms, and it is one of the first essential tools in IGCSE algebra.
在代数中，字母代表未知或变化的量。像 3x + 5y - 2x + 7 这样的表达式由多个被称为“项”的部分组成。为了让表达式更短、更易使用，我们把变量部分完全相同的项合并起来。这项技能称为合并同类项，是 IGCSE 代数中最初的基本工具之一。
1. Algebraic Terms and Coefficients | 代数项与系数
A term is a single number, a single letter, or a product of numbers and letters. In 3x + 5y - 2x + 7, the terms are 3x, 5y, -2x and 7. The number multiplying the variable is called the coefficient: in 3x the coefficient is 3, in -2x the coefficient is -2, and in 5y the coefficient is 5. A term with no variable, such as 7, is called a constant.
一个项可以是一个数、一个字母，或数与字母的乘积。在 3x + 5y - 2x + 7 中，各项分别是 3x、5y、-2x 和 7。乘以变量的数称为系数：3x 的系数为 3，-2x 的系数为 -2，5y 的系数为 5。不含变量的项（如 7）称为常数项。
When a term is written as x, its coefficient is 1; when it is written as -x, its coefficient is -1. This hidden coefficient often causes errors in simplification.
当一项写作 x 时，它的系数是 1；写作 -x 时，系数是 -1。这种隐藏系数经常导致化简错误。
2. What Are Like Terms? | 什么是同类项
Like terms are terms whose variable parts are identical. The variables must be the same letters, and each letter must be raised to the same power. For example, 4x and -7x are like terms because both contain exactly x to the power 1. Similarly, 2x² and 5x² are like terms because both contain x².
同类项是变量部分完全相同的项。变量必须是相同的字母，并且每个字母的指数也必须相同。例如，4x 和 -7x 是同类项，因为两者都恰好含有 x 的一次方。同样，2x² 和 5x² 是同类项，因为两者都含有 x²。
Coefficients do not need to match. 9ab and -3ab are like terms even though 9 and -3 are different numbers. It is the variable part, not the number part, that decides whether terms are like.
系数不需要相同。9ab 和 -3ab 是同类项，尽管 9 和 -3 是不同的数。决定项是否同类的依据是变量部分，而不是数字部分。
3. Identifying Like and Unlike Terms | 识别同类项与异类项
Terms that look similar may still be unlike. For example, 3x and 3x² are unlike because the powers of x are different. The terms 4xy and 4x are unlike because the first has two variables, x and y, while the second has only x. Also, 2x²y and 2xy² are unlike because the power 2 is attached to different letters.Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com
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