(a+b) FOIL 展开计算器（两个二项式相乘）FOIL Calculator (Multiply Two Binomials)
把 (ax + b)(cx + d) 按 FOIL 法展开：首项 (First)、外项 (Outer)、内项 (Inner)、末项 (Last) 分别相乘，再合并同类项得到 acx² + (ad + bc)x + bd。可以改变量名，也可以代入 x 的值求结果。本地处理。Expand (ax + b)(cx + d) by FOIL: multiply the First, Outer, Inner and Last terms, then combine like terms to get acx² + (ad + bc)x + bd. You can rename the variable and substitute a value of x. Processed locally.
使用说明与常见问题How-to & FAQ
「FOIL 展开计算器（两个二项式相乘）」是什么？What is the FOIL Calculator (Multiply Two Binomials) tool?
把 (ax + b)(cx + d) 按 FOIL 法展开：首项 (First)、外项 (Outer)、内项 (Inner)、末项 (Last) 分别相乘，再合并同类项得到 acx² + (ad + bc)x + bd。可以改变量名，也可以代入 x 的值求结果。本地处理。Expand (ax + b)(cx + d) by FOIL: multiply the First, Outer, Inner and Last terms, then combine like terms to get acx² + (ad + bc)x + bd. You can rename the variable and substitute a value of x. Processed locally.
如何使用「FOIL 展开计算器（两个二项式相乘）」？How do I use the FOIL Calculator (Multiply Two Binomials) tool?
在「FOIL 展开计算器（两个二项式相乘）」中，填写「a（第一个括号 x 的系数）」、「b（第一个括号常数）」、「c（第二个括号 x 的系数）」、「d（第二个括号常数）」、「变量名」等参数，结果会随输入实时计算并显示在下方。In the FOIL Calculator (Multiply Two Binomials): Fill in "a (x coefficient, first bracket)", "b (constant, first bracket)", "c (x coefficient, second bracket)", "d (constant, second bracket)", "Variable name"; results are recalculated instantly as you type.
FOIL 是什么意思？What does FOIL stand for?
First（首项相乘）、Outer（外侧两项相乘）、Inner（内侧两项相乘）、Last（末项相乘），是两个二项式相乘时不漏项的记忆方法。First, Outer, Inner, Last: a way to remember every product when multiplying two binomials.
展开后怎么合并？How are the terms combined?
外项和内项都是一次项，合并为 (ad + bc)x，所以 (ax + b)(cx + d) = acx² + (ad + bc)x + bd。例如 (x − 3)(x + 3) 的一次项抵消，得到 x² − 9。The Outer and Inner products are both x terms and combine to (ad + bc)x, so (ax + b)(cx + d) = acx² + (ad + bc)x + bd. In (x − 3)(x + 3) they cancel, giving x² − 9.
三项式也能用吗？Does it work for trinomials?
FOIL 只适用于两个二项式。多项式相乘需要用分配律把每一项分别相乘。FOIL only covers two binomials. Larger polynomials need the distributive law, multiplying every term by every term.
能举个计算实例吗？Can you show a worked example?
例如在「FOIL 展开计算器（两个二项式相乘）」中填 a（第一个括号 x 的系数） = 2，b（第一个括号常数） = 3，c（第二个括号 x 的系数） = 4，d（第二个括号常数） = 5，变量名 = x，代入的值（可选） = 1，结果区显示：原式：(2x + 3)(4x + 5)；F 首项 ax·cx：8x²；O 外项 ax·d：10x；I 内项 b·cx：12x；L 末项 b·d：15；展开合并：8x² + 22x + 15；x = 1 时：45For example, entering a (x coefficient, first bracket) = 2, b (constant, first bracket) = 3, c (x coefficient, second bracket) = 4, d (constant, second bracket) = 5, Variable name = x, Value to substitute (optional) = 1 in the FOIL Calculator (Multiply Two Binomials) gives: Expression: (2x + 3)(4x + 5); F First ax·cx: 8x²; O Outer ax·d: 10x; I Inner b·cx: 12x; L Last b·d: 15; Expanded: 8x² + 22x + 15; At x = 1: 45
哪些输入会被检查？Which inputs are validated?
「FOIL 展开计算器（两个二项式相乘）」会检查这些输入——「a（第一个括号 x 的系数）」、「b（第一个括号常数）」、「c（第二个括号 x 的系数）」、「d（第二个括号常数）」：必须填写；「代入的值（可选）」：可留空；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The FOIL Calculator (Multiply Two Binomials) checks its inputs — "a (x coefficient, first bracket)", "b (constant, first bracket)", "c (x coefficient, second bracket)", "d (constant, second bracket)": required; "Value to substitute (optional)": optional; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.
有哪些选项可以调整？What options can I adjust?
「FOIL 展开计算器（两个二项式相乘）」的设置：「a（第一个括号 x 的系数）」默认 2；「b（第一个括号常数）」默认 3；「c（第二个括号 x 的系数）」默认 4；「d（第二个括号常数）」默认 5；「变量名」默认 x；「代入的值（可选）」默认 1。每次生成结果都按当前设置处理。Settings in the FOIL Calculator (Multiply Two Binomials) — "a (x coefficient, first bracket)" default 2; "b (constant, first bracket)" default 3; "c (x coefficient, second bracket)" default 4; "d (constant, second bracket)" default 5; "Variable name" default x; "Value to substitute (optional)" default 1. The result always uses the current settings.
计算精度如何？How precise are the results?
「FOIL 展开计算器（两个二项式相乘）」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The FOIL Calculator (Multiply Two Binomials) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「FOIL 展开计算器（两个二项式相乘）」免费吗？需要注册吗？Is the FOIL Calculator (Multiply Two Binomials) free? Do I need an account?
「FOIL 展开计算器（两个二项式相乘）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The FOIL Calculator (Multiply Two Binomials) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.