{"id":65118,"date":"2025-08-18T10:11:10","date_gmt":"2025-08-18T07:11:10","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=65118"},"modified":"2026-10-26T09:28:36","modified_gmt":"2026-10-26T06:28:36","slug":"foil-method","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/foil-method\/","title":{"rendered":"FOIL Calculator \u2013 Multiply Binomials Step by Step"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Expand Binomials Using the FOIL Method<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"65118\" data-favorite-title=\"FOIL\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/foil-method\/\" data-favorite-excerpt=\"Expand the product of two binomials with the FOIL method (First, Outer, Inner, Last). Enter expressions like x + 2 and x + 3, and get the simplified quadratic result instantly.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-algebra\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/mathematics\/foil-method\/\" method=\"POST\" class=\"calculator\" id=\"calculator-65118\" data-post=\"65118\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">First binomial (a + b)<\/label><input type=\"text\" name=\"first_binomial_a_b\" id=\"field-1\" aria-describedby=\"calc-info-1\" step=\"any\" value=\"x + 2\"\/><small id=\"calc-info-1\">Enter a binomial like x + 2 or 3x - 5<\/small><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">Second binomial (c + d)<\/label><input type=\"text\" name=\"second_binomial_c_d\" id=\"field-2\" aria-describedby=\"calc-info-2\" step=\"any\" value=\"x + 3\"\/><small id=\"calc-info-2\">Enter another binomial like x + 3 or 2x - 4<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"65118\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Expanded expression<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copy link to this calculation<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"65118\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">1<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>FOIL Expansion Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[(a + b)(c + d) = ac + ad + bc + bd\\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(a\\) and \\(b\\) \u2014 the two terms of the first binomial<\/li>\n<li>\\(c\\) and \\(d\\) \u2014 the two terms of the second binomial<\/li>\n<\/ul>\n<p>The four products correspond to the letters of FOIL:<\/p>\n<ul>\n<li><strong>F<\/strong>irst: \\(a \\cdot c\\) \u2014 the first terms of each binomial<\/li>\n<li><strong>O<\/strong>uter: \\(a \\cdot d\\) \u2014 the outermost terms<\/li>\n<li><strong>I<\/strong>nner: \\(b \\cdot c\\) \u2014 the innermost terms<\/li>\n<li><strong>L<\/strong>ast: \\(b \\cdot d\\) \u2014 the last terms of each binomial<\/li>\n<\/ul>\n<p>After multiplying, combine the like terms \u2014 usually the Outer and Inner products \u2014 to obtain the simplified expression.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>FOIL \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> expand \\((x + 2)(x + 3)\\) using the FOIL method.<\/p>\n<p>\\[ \\text{First: } x \\cdot x = x^2 \\]&lt;\/n<\/p>\n<p>\\[ \\text{Outer: } x \\cdot 3 = 3x \\]<\/p>\n<p>\\[ \\text{Inner: } 2 \\cdot x = 2x \\]<\/p>\n<p>\\[ \\text{Last: } 2 \\cdot 3 = 6 \\]<\/p>\n<p>Combine the like terms \\(3x\\) and \\(2x\\):<\/p>\n<p>\\[ x^2 + 3x + 2x + 6 = x^2 + 5x + 6 \\]<\/p>\n<p><strong>Result:<\/strong> \\(x^2 + 5x + 6\\)<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the FOIL Calculator<\/h2>\n<ol>\n<li>Type the first binomial into the <strong>First binomial (a + b)<\/strong> field, for example <code>x + 2<\/code> or <code>3x - 5<\/code>.<\/li>\n<li>Type the second binomial into the <strong>Second binomial (c + d)<\/strong> field, such as <code>x + 3<\/code> or <code>2x - 4<\/code>.<\/li>\n<li>Make sure both binomials use the same variable letter.<\/li>\n<li>The <strong>Expanded expression<\/strong> field updates automatically, showing the simplified product.<\/li>\n<\/ol>\n<h2>What Is the FOIL Method?<\/h2>\n<p>FOIL is a mnemonic for <strong>First, Outer, Inner, Last<\/strong> \u2014 the order in which you multiply the terms when expanding the product of two binomials. It is simply an organized way of applying the distributive property twice:<\/p>\n<p>\\[ (a + b)(c + d) = a(c + d) + b(c + d) = ac + ad + bc + bd \\]<\/p>\n<p>Multiplying binomials appears everywhere in algebra: it is how quadratic expressions are built, how equations are rewritten before solving, and how many factoring problems are reversed. For example, \\(x^2 + 5x + 6\\) factors back into \\((x + 2)(x + 3)\\), and FOIL is the quickest way to verify such a factorization.<\/p>\n<p>The result of FOIL on two linear binomials is always a quadratic of the form \\(Ax^2 + Bx + C\\). The middle coefficient \\(B\\) is the sum of the Outer and Inner products \u2014 this is exactly the sum you look for when factoring a quadratic by inspection. If you then need to solve \\(Ax^2 + Bx + C = 0\\), the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/quadratic-equation-2\/\">Quadratic Equation Calculator<\/a> or the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/discriminant-quadratic-equation\/\">Discriminant of a Quadratic Equation Calculator<\/a> can take it from there.<\/p>\n<h2>Assumptions, Limitations and Tips<\/h2>\n<ul>\n<li><strong>Two binomials only.<\/strong> FOIL works for products of two expressions with two terms each, like \\((2x - 1)(x + 4)\\). For longer polynomials, use repeated distribution or a general <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/multiplying-binomials\/\">Multiplying Binomials Calculator<\/a> as a starting point, then distribute term by term.<\/li>\n<li><strong>Same variable required.<\/strong> This calculator expects both binomials to use the same letter, e.g. both in \\(x\\). Mixing variables like \\(x + 2\\) and \\(y + 3\\) will return an error.<\/li>\n<li><strong>Accepted formats.<\/strong> Enter terms with an explicit coefficient (<code>3x<\/code>), an implied coefficient of 1 (<code>x<\/code>), or a constant only. Subtraction is written with a minus sign, e.g. <code>3x - 5<\/code>.<\/li>\n<li><strong>Watch the signs.<\/strong> When both binomials contain subtraction, the Outer and Inner products are negative. For example, \\((x - 2)(x - 3) = x^2 - 3x - 2x + 6 = x^2 - 5x + 6\\).<\/li>\n<li><strong>Combine like terms.<\/strong> The raw FOIL output has four terms; always add the Outer and Inner products (the two middle terms) to simplify. This calculator does that step for you.<\/li>\n<li><strong>Special patterns.<\/strong> Products like \\((x + a)^2\\) give perfect square trinomials, and \\((a + b)(a - b)\\) gives a difference of squares where the middle terms cancel \u2014 useful shortcuts to recognize when checking your answer.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Expand the product of two binomials with the FOIL method (First, Outer, Inner, Last). Enter expressions like x + 2 and x + 3, and get the simplified quadratic result instantly.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7],"tags":[11],"class_list":["post-65118","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-algebra"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65118","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=65118"}],"version-history":[{"count":4,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65118\/revisions"}],"predecessor-version":[{"id":67534,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65118\/revisions\/67534"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=65118"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=65118"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=65118"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}