📚 Collecting Like Terms | 合并同类项
In algebra, expressions such as 3x + 5x can be simplified. The operation shown is addition, and the parts being added are called terms. Collecting like terms means combining terms that have exactly the same variable part, so that the whole expression is written in a simpler but equivalent form.
在代数中，像 3x + 5x 这样的式子可以化简。这里进行的运算是加法，被相加的部分称为“项”。合并同类项就是把变量部分完全相同的项合并在一起，使整个式子写成更简单但等价的形态。
1. What Are Like Terms? | 什么是同类项
A term is a number, a variable, or a product of numbers and variables. For example, in the expression 4x² + 3x – 2, the terms are 4x², 3x and -2.
“项”是一个数、一个变量，或数与变量的乘积。例如，在 4x² + 3x – 2 中，各项分别是 4x²、3x 和 -2。
Two terms are called like terms when they have exactly the same variable part. The numbers in front of the variables, called coefficients, may be different.
当两项的变量部分完全相同时，它们称为同类项；系数可以不同。
For example, 3x and 5x are like terms because both contain x. However, 3x and 5x² are not like terms because x and x² are different variable parts.
例如，3x 和 5x 是同类项，因为它们都含有 x；而 3x 和 5x² 不是同类项，因为 x 和 x² 是不同变量部分。
Here are some pairs of like and unlike terms:
下面是一些同类项与非同类项的对比：
| Like terms 同类项 | Unlike terms 非同类项 |
| 2a and 7a | 2a and 2b |
| 4xy and -xy | 4xy and 4x²y |
| 3p² and -p² | 3p
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