📚 Algebraic Expressions, Equations and Formulae | 代数表达式、方程与公式
Algebra is the branch of mathematics that uses letters and symbols to represent numbers and relationships. In Key Stage 3, you will learn how to simplify expressions, solve equations, substitute values and model real-life problems. This article covers all the essential skills for Cambridge KS3 algebra.
代数是使用字母和符号表示数字和关系的数学分支。在关键阶段三（KS3），你将学习如何化简表达式、解方程、代入求值以及构建现实问题的模型。本文涵盖了剑桥 KS3 代数部分的所有核心技巧。
1. Algebraic Expressions and Terms | 代数表达式与项
An algebraic expression is a combination of numbers, letters (variables) and operation symbols such as +, -, x, ÷. For example, 3a + 2b - 7 is an expression. Expressions do not contain an equals sign.
代数表达式是由数字、字母（变量）和运算符号如 +、-、x、÷ 组成的式子。例如 3a + 2b - 7 是一个表达式。表达式不包含等号。
A term is a single number, a variable, or numbers and variables multiplied together. Terms are separated by + or - signs. In 5x² - 3y + 4, the terms are 5x², -3y, and 4.
项是一个单独的数、一个变量，或者数字与变量的乘积。项之间由加号或减号分隔。在 5x² - 3y + 4 中，项分别为 5x²、-3y 和 4。
The coefficient is the number part of a term that contains a variable. In the term 7m, the coefficient is 7. If no number is written, the coefficient is 1 (e.g., x has coefficient 1).
系数是含有变量的项中的数字部分。在 7m 这项中，系数为 7。如果没有写数字，则系数为 1（例如 x 的系数为 1）。
2. Collecting Like Terms | 合并同类项
Like terms are terms that have exactly the same variable(s) raised to the same power. Only the coefficients can differ. For instance, 2x and -5x are like terms, while 3x and 3x² are not.
同类项是指变量及其指数完全相同的项，只有系数可以不同。例如 2x 和 -5x 是同类项，而 3x 和 3x² 不是同类项。
their coefficients. Simplify 4a + 3b - a + 2b by grouping: (4a - a) + (3b + 2b) = 3a + 5b.
化简表达式时，你需要合并同类项，将系数相加或相减。化简 4a + 3b - a + 2b：分组为 (4a - a) + (3b + 2b) = 3a + 5b。
Always check that you have combined all like terms and that no further simplification is possible. The simplified expression should have no parentheses and no like terms remaining.
始终检查是否已合并所有同类项且无法进一步化简。化简后的表达式应不含括号，且没有剩余的同类项。
3. Expanding Brackets | 展开括号
ve law states a(b + c) = a x b + a x c. For example, 3(2x + 5) = 3 x 2x + 3 x 5 = 6x + 15.
展开括号是指将括号内的每一项与括号外的项相乘。分配律为 a(b + c) = a x b + a x c。例如 3(2x + 5) = 3 x 2x + 3 x 5 = 6x + 15。
When the outside term is negative
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