📚 9C Unit 3 Algebraic Expressions and Linear Equations | 9C 第3单元 代数表达式与一次方程
Welcome to this revision guide for 9C Unit 3 on algebraic expressions and linear equations. This unit focuses on manipulating algebraic symbols, simplifying and expanding expressions, factorising common factors, solving equations, rearranging formulas and interpreting inequalities. Mastering these skills is essential for success in secondary mathematics, because they form the foundation for functions, graphs and problem solving in later units.
欢迎阅读 9C 第 3 单元复习指南，本单元聚焦代数表达式与一次方程。内容包括代数符号运算、表达式的化简与展开、提取公因式、方程求解、公式变形以及不等式解释。掌握这些技能对中学数学的后续学习至关重要，因为它们是函数、图像和综合问题解决的基础。
1. What Is an Algebraic Expression? | 什么是代数表达式？
An algebraic expression is a combination of numbers, variables and operation symbols that represents a mathematical quantity. For example, 3x + 5 is an expression with one variable x, a term with coefficient 3, and a constant term 5. Expressions do not contain an equals sign; that is the key difference between an expression and an equation.
代数表达式是由数字、变量和运算符号组成的数学式子，用来表示一个数量。例如 3x + 5 是一个含变量 x 的表达式，其中 3 是 x 的系数，5 是常数项。表达式不包含等号，这是表达式与方程最关键的区别。
The parts of an expression have special names. A variable is a letter that stands for an unknown or changing number. A term is a single number, a variable or a product of them, such as 4x, −7 or 2ab. A coefficient is the numerical factor multiplying a variable, and a constant term contains no variable.
表达式中的各部分有专门名称。变量是代表未知量或变化量的字母；项是单独的数字、变量或它们的乘积，例如 4x、−7 或 2ab；系数是乘在变量前的数字因数；常数项不含任何变量。
ution is a useful check after simplifying or factorising, because the original and the new form must give the same value.
表达式可以通过代入数值来求值。若 x = 4，则 3x + 5 = 3 × 4 + 5 = 17。化简或因式分解之后，代入数值检验非常有用，因为原式与变形后的式子必须给出相同的值。
3x + 5 = 3 × 4 + 5 = 17 when x = 4
2. Terms, Coefficients and Like Terms | 项、系数与同类项
Like terms contain exactly the same variable part with the same powers. For example, 3x and −7x are like terms, and 5a²b and 2a²b are like terms. By contrast, 3x and 3x² are not like terms, and 4a and 4b are not like terms because the variable letters are different.
同类项必须含有完全相同的字母部分，且指数也相同。例如 3x 与 −7x 是同类项，5a²b 与 2a²b 也是同类项。相反，3x 与 3x² 不是同类项，4a 与 4b 因字母不同也不是同类项。
Look at the expression 4x² + 3x − 7. It has three terms. The first term has coefficient 4 and variable part x²; the second has coefficient 3 and variable part x; the third is a constant term.
观察表达式 4x² + 3x − 7，它有三项。第一项的系数是 4，字母部分是 x²；第二项的系数是 3，字母部分是 x；第三项是常数项。
| Term 项 | Coefficient 系数 | Variable part 字母部分 |
| 4x² | 4 | x² |
| 3x | 3 | x |
| −7 | 无 none | 常数项 constant |
Remember that a term keeps the sign in front of it. In 5x − 8y + 3, the terms are 5x, −8y and +3, not 8y and 3. Keeping signs with terms prevents errors when collecting like terms.
要记住，项前面的符号属于该项。在 5x − 8y + 3 中，项是 5x、−8y 和 +3，而不是 8y 和 3。把符号与项一起看，能避免合并同类项时的错误。
3. Simplifying Expressions by Collecting Like Terms | 合并同类项化简表达式
To simplify an expression, collect like terms by adding or subtracting their coefficients while keeping the variable part unchanged. The expression 7a + 3b − 2a + 5b simplifies in two groups: the a terms and the b terms.
化简表达式时，把同类项的系数相加或相减，字母部分保持不变。表达式 7a + 3b − 2a + 5b 可以分成 a 项和 b 项两组来化简。
7a + 3b − 2a + 5b = (7a − 2a) + (3b + 5b) = 5a + 8b
x² + 8x. The x² terms and the x terms are collected separately because they are not like terms.
第二个例子含有指数：5x² + 2x − 3x² + 6x = (5x² − 3x²) + (2x + 6x) = 2x² + 8x。x² 项与 x 项必须分开合并，因为它们不是同类项。
A common mistake is to combine terms that are not like terms, for example writing 3x + 2 as 5x. This is wrong because 3x and 2 are unlike terms. Another mistake is to lose a negative sign, so write every step clearly on a new line.
常见错误之一是把非同类项合并，例如把 3x + 2 写成 5x，这是错误的，因为 3x 与
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