Collecting Like Terms | 合并同类项

📚 Collecting Like Terms | 合并同类项

In algebra, expressions often contain many terms. Collecting like terms is the process of simplifying an expression by adding or subtracting terms that have the same variable part.

在代数中，表达式通常包含许多项。合并同类项就是通过加减具有相同变量部分的项来化简表达式的过程。

1. What is a Term? | 什么是项？

An algebraic expression is built from terms. Terms are separated by plus (+) or minus (-) signs. For example, in the expression 4x² – 3x + 7, the terms are 4x², -3x and 7.

代数表达式由项构成。项之间用加号 (+) 或减号 (-) 分隔。例如，在表达式 4x² – 3x + 7 中，项是 4x²、-3x 和 7。

Each term has a coefficient and a variable part. The coefficient is the number in front of the variable. If no number is written, the coefficient is 1 or -1.

每一项都包含系数和变量部分。系数是变量前面的数字。如果没有写数字，则系数为 1 或 -1。

x = 1x, -y = -1y

For instance, x is the same as 1x, and -y is the same as -1y. Recognising the hidden coefficient 1 is essential when collecting like terms.

例如，x 与 1x 相同，-y 与 -1y 相同。识别隐藏的系数 1 对于合并同类项至关重要。

2. Identifying Like Terms | 识别同类项

Like terms have exactly the same variable part. The variable part must contain the same letters raised to the same powers.

同类项具有完全相同的变量部分。变量部分必须包含相同的字母以及相同的幂次。

• Examples of like terms: 3x and 8x; 5x² and -2x²; 4ab and 7ab.

  同类项的例子：3x 和 8x；5x² 和 -2x²；4ab 和 7ab。

• Examples of unlike terms: 3x and 3x²; 2xy and 2x²y; a and b.

  异类项的例子：3x 和 3x²；2xy 和 2x²y；a 和 b。

Only the coefficients may be different. The variable part must be identical before terms can be combined.

只有系数可以不同。只有当变量部分完全相同时，各项才能合并。

3. The Rule for Collecting Like Terms | 合并同类项的法则

To collect like terms, add or subtract their coefficients and keep the variable part

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