Simplifying Algebraic Expressions | 代数表达式化简

📚 Simplifying Algebraic Expressions | 代数表达式化简

In KS3 Cambridge Mathematics, simplifying algebraic expressions is one of the most important algebra skills. You need to recognise like terms, expand brackets, factorise simple expressions, and substitute values correctly. This article explains each skill step by step with clear worked examples.

在 KS3 剑桥数学中，化简代数表达式是最重要的代数技能之一。你需要识别同类项、展开括号、因式分解简单表达式，并正确代入数值。本文将逐步讲解每项技能，并配以清晰的例题。

1. Understanding Terms and Coefficients | 理解项与系数

An algebraic expression is a combination of numbers, variables, and operations. For example, 5x + 3y − 7 is an expression. Each part separated by ‘+’ or ‘−’ is called a term. In 5x + 3y − 7, the terms are 5x, 3y, and −7.

代数表达式是数字、变量和运算的组合。例如，5x + 3y − 7 是一个表达式。由 ‘+’ 或 ‘−’ 分隔的每一部分称为一项。在 5x + 3y − 7 中，项为 5x、3y 和 −7。

The number multiplying a variable is called the coefficient. In the term 5x, the coefficient is 5. If a term is written as x, the coefficient is 1. A term without a variable, such as −7, is called a constant term.

乘以变量的数称为系数。在项 5x 中，系数为 5。如果一项写作 x，其系数为 1。不含变量的项（如 −7）称为常数项。

Here are the main vocabulary words you need to know:

以下是你需要了解的主要词汇：

• Variable: a symbol, such as x or y, that represents an unknown number.
• 变量：一个符号，如 x 或 y，代表未知数。
• Coefficient: the number multiplied by the variable.
• 系数：乘以变量的数。
• Constant: a fixed number, such as 5 or −3.
• 常数：一个固定的数，如 5 或 −3。
• Term: a single number, variable, or product of numbers and variables.
• 项：单个数字、变量，或数字与变量的乘积。

2. Collecting Like Terms | 合并同类项

Like terms have exactly the same variable part, including the same power. For instance, 4x and 9x are like terms, but 4x and 4x² are not like terms. You can add or subtract like terms by adding or subtracting their coefficients.

同类项具有完全相同的变量部分，包括相同的幂。例如，4x 和 9x 是同类项，但 4x 和 4x² 不是同类项。你可以通过加减系数来合并同类项。

Example: Simplify 7a + 3b − 2a + 5b.

示例：化简 7a + 3b − 2a + 5b。

7a + 3b − 2a + 5b = (7a − 2a) + (