Unit 2: Algebraic Expressions and Linear Equations | 第2单元：代数表达式与线性方程

📚 Unit 2: Algebraic Expressions and Linear Equations | 第2单元：代数表达式与线性方程

Welcome to the Unit 2 revision guide. This unit focuses on algebraic expressions, expanding brackets, substituting into formulas, and solving linear equations. These skills are essential for Key Stage 3 and IGCSE Foundation Mathematics, and they appear in both calculator and non-calculator papers.

欢迎阅读第2单元复习指南。本单元重点涵盖代数表达式、去括号、代入公式以及解一元一次方程。这些技能是初中数学与 IGCSE 基础数学的核心内容，在可使用计算器和不可使用计算器的试卷中都会考查。

1. Understanding Algebraic Terms | 理解代数术语

In algebra, a term is a single number, letter, or product of numbers and letters. For example, 5xy is a term, while x + 4 is an expression with two terms. The coefficient is the number in front of the variable; in 7a, the coefficient is 7. A constant is a term with no variable, such as -3.

在代数中，项是一个单独的数、字母或数字与字母的乘积。例如，5xy 是一项，而 x + 4 是含有两个项的表达式。系数是变量前面的数；在 7a 中，系数是 7。常数是不含变量的项，例如 -3。

An expression does not contain an equals sign, but an equation does. For example, 2x + 5 is an expression, while 2x + 5 = 13 is an equation. Knowing this difference helps you choose the correct method in a question.

表达式不含有等号，而方程含有等号。例如，2x + 5 是表达式，而 2x + 5 = 13 是方程。了解这一区别有助于你在解题时选择正确的方法。

Terms can also contain powers. The term 4x² has the variable x raised to the power 2, and its coefficient is 4. A term like x has an invisible coefficient of 1, and -x has a coefficient of -1.

项还可以包含幂。项 4x² 中的变量 x 的指数为 2，其系数为 4。像 x 这样的项系数是隐形的 1，而 -x 的系数是 -1。

2. Collecting Like Terms | 合并同类项

Like terms have exactly the same variable part raised to the same power. We can add or subtract the coefficients but keep the variable part unchanged. For instance, 3a + 5a = 8a, but 3a + 5b cannot be simplified further.

同类项具有完全相同的变量部分且指数相同。我们可以加减系数，但变量部分保持不变。例如，3a + 5a = 8a，但 3a + 5b 不能进一步化简。

To simplify 4x + 2y – x + 3y, first group the like terms: (4x – x) + (2y + 3y). This gives 3x + 5y. Always pay attention to the sign in front of each term.

化简 4x + 2y – x + 3y 时，首先将同类项分组：(4x – x) + (2y + 3y)。结果为 3x + 5y。始终注意每一项前面的符号。

4x + 2y – x + 3y = 3x + 5y

Terms with different powers are not like terms. For example, 2x and 3x² cannot be combined because the exponents are different. Similarly, xy and x are not like terms.

指数不同的项不是同类项。例如，2x 和 3x² 不能合并，因为指数不同。同样，xy 和 x 也不是同类项。

3. Expanding Single Brackets | 单项展开括号

When expanding a single bracket, multiply every term inside the bracket by the term outside. This uses the distributive law: a(b + c) = ab + ac.

展开单项括号时，将括号内的每一项都乘以外面的项。这运用分配律：a(b + c) = ab + ac。

a(b + c) = ab + ac

Example: expand 2(3x – 5). Multiply 2 by 3x to get 6x, and multiply 2 by -5 to get -10. The result is 6x – 10.

示例：展开 2(3x – 5)。2 乘以 3x 得 6x，2 乘以 -5 得 -10。结果为 6x – 10。

2(3x – 5) = 6x – 10

If a negative sign is outside the bracket, it changes the sign of every term inside. For -3(2x + 4), the expansion is -6x – 12, not -6x + 12.

如果括号外是负号，它会改变括号内每一项的符号。对于 -3(2x + 4)，展开结果为 -6x – 12，而不是 -6x + 12。

4. Expanding Double Brackets | 双括号展开

To expand two brackets such as (x + 3)(x + 2), use the FOIL method: multiply the First terms, Outer terms, Inner terms, and Last terms. This gives x² + 2x + 3x + 6, which simplifies to x² + 5x + 6.

展开两个括号（如 (x + 3)(x + 2)）时，可用 FOIL 法则：分别相乘首项、外项、内项和末项。得到 x² + 2x + 3x + 6，化简为 x² + 5x + 6。

(x + 3)(x + 2) = x² + 5x + 6

Remember that the signs matter. For (x – 4)(x + 5), the expansion is x² +

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