🍎 合并同类项：同类才能相加🍎 Combining Like Terms: Same Family Only
上一片里，字母像小盒子，装着不知道的数，我们把这样的式子叫代数式。可式子一长就乱了：3x + 2 + 2x + 5 里，哪些能加、哪些不能加？这一片把混乱理成一家人。Last leaf, letters became little boxes holding unknown numbers — that's an algebraic expression. But long expressions get messy: in 3x + 2 + 2x + 5, what may add together and what may not? This leaf sorts the mess into families.
第 1 步：苹果归苹果，橘子归橘子Step 1: Apples with apples, oranges with oranges
先从最熟悉的水果开始——为什么 3 个苹果加 2 个橘子，不能叫 5 个“苹果橘”？Start with familiar fruit — why can't 3 apples plus 2 oranges be called 5 “apploranges”?
苹果和橘子长得不一样，谁也变不成谁，只能各数各的：3 个苹果 + 2 个苹果 = 5 个苹果；3 个苹果 + 2 个橘子 = 还是 3 个苹果和 2 个橘子。代数式里的项也是这样——字母部分完全相同的项（比如 3x 和 2x）才叫同类项，才是一家人。Apples and oranges are simply not the same stuff — nothing turns one into the other, so each is counted on its own: 3 apples + 2 apples = 5 apples; 3 apples + 2 oranges = still 3 apples and 2 oranges. Terms work the same way: only terms with exactly the same letter part (like 3x and 2x) are like terms — one family.
都是一家人了，那怎么把它们合起来？Once you know who is family, how do you merge them?
第 2 步：合并时，只动系数Step 2: Merging only touches the coefficients
3x + 2x：字母都是 x，是一家人，把系数 3 和 2 相加——(3 + 2)x = 5x，五块 x 方块并成一排。而 3x + 2y 里字母不同，两家人凑不到一起，只能原样摆着。常数项也是一族：2 + 5 = 7，和字母项各算各的。3x + 2x: both have the letter x — one family — so add the coefficients: (3 + 2)x = 5x, and five x-tiles merge into a single row. But 3x + 2y has different letters: two families that never mix. Plain numbers (constant terms) form their own family too: 2 + 5 = 7, counted apart from the letter terms.
那就没有陷阱了吗？有——字母相同还不够。So no traps left? There's one — the same letter is not enough.
第 3 步：一眼认出同类项Step 3: Spotting like terms at a glance
关键看“字母部分”是否一模一样：3x 和 5x 同类；x 和 x² 不是（一个是一次、一个是平方）；x 和 y 也不是。检查时就像分卡片：把颜色、字母、指数都相等的放到同一堆，合并前先圈出同类项，再一族一族地加。Check the whole letter part: 3x and 5x are like terms; x and x² are not (one is linear, one is squared); x and y are not, either. Sort them like cards: same colour, same letter, same exponent go into one pile. Before merging, circle the like terms — then add family by family.
🎮 你来给项分家（30 秒）🎮 Your turn: sort the families (30 seconds)
规则很简单：点两张卡，同族就会牵手合并；不是同族会被摇头拒绝。一共四关，从易到难。The rule is simple: tap two cards — same family, they hold hands and merge; different family, they shake their heads. Four levels, easy to tricky.
一句话记住它：合并同类项，就是只把同类项的系数相加，字母部分原样不动；判定标准是“字母部分完全相同”——字母相同、指数也相同。Remember it in one line: combining like terms adds only the coefficients and leaves the letter part untouched; “like” means exactly the same letter part — same letter, same exponent.
3x + 2x = 5x；3x + 2y 不能合并（字母不同）3x + 2x = 5x; 3x + 2y can't merge (different letters)常数项自成一族：2 + 5 = 7，与字母项分开算Constant terms are a family of their own: 2 + 5 = 7, kept apart from letter termsx 和 x² 不是同类项（指数不同）；合并前先圈出同类项x and x² are not like terms (different exponents); circle the like terms first
内容参考 OpenStax 等公开教材，多来源核对 · AI 生成、人工审核 · 发现错误欢迎指正，帮这片叶子长得更好。Based on OpenStax and other open textbooks, cross-checked across sources · AI-generated, human-reviewed · Spotted a mistake? Tell us — help this leaf grow.
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