{"id":365,"date":"2026-10-03T13:59:29","date_gmt":"2026-10-03T12:59:29","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/foil-yontemi\/"},"modified":"2026-10-03T13:59:29","modified_gmt":"2026-10-03T12:59:29","slug":"foil-yontemi","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/matematik\/foil-yontemi\/","title":{"rendered":"FOIL Y\u00f6ntemi Hesaplama Arac\u0131"},"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\">FOIL Y\u00f6ntemi ile Binomlar\u0131 A\u00e7\u0131n<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"365\" data-favorite-title=\"FOIL\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/matematik\/foil-yontemi\/\" data-favorite-excerpt=\"FOIL y\u00f6ntemi (First, Outer, Inner, Last \u2014 \u0130lk, D\u0131\u015f, \u0130\u00e7, Son) ile iki binomun \u00e7arp\u0131m\u0131n\u0131 a\u00e7\u0131n. x + 2 ve x + 3 gibi ifadeleri girin ve sadele\u015ftirilmi\u015f ikinci derece sonucu an\u0131nda al\u0131n.\" aria-label=\"Favorilere ekle\" 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\/tr\/matematik\/foil-yontemi\/\" method=\"POST\" class=\"calculator\" id=\"calculator-365\" data-post=\"365\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Birinci binom (a + b)<\/label><input type=\"text\" name=\"birinci_binom_a_b\" id=\"field-1\" aria-describedby=\"calc-info-1\" step=\"any\" value=\"x + 2\"\/><small id=\"calc-info-1\">x + 2 veya 3x - 5 gibi bir binom girin<\/small><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">\u0130kinci binom (c + d)<\/label><input type=\"text\" name=\"kinci_binom_c_d\" id=\"field-2\" aria-describedby=\"calc-info-2\" step=\"any\" value=\"x + 3\"\/><small id=\"calc-info-2\">x + 3 veya 2x - 4 gibi ba\u015fka bir binom girin<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"365\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/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> Sonu\u00e7lar\u0131n\u0131z<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>A\u00e7\u0131lm\u0131\u015f ifade<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><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\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/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>Yorum b\u0131rak<\/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=\"365\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/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\">Be\u011fendim <\/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\">Faydal\u0131 <\/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\">Kafam kar\u0131\u015ft\u0131 <\/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\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/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\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Hatal\u0131 <\/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 A\u00e7\u0131l\u0131m Form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/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>Burada:<\/strong><\/p>\n<ul>\n<li>\\(a\\) ve \\(b\\) \u2014 ilk binomun iki terimi<\/li>\n<li>\\(c\\) ve \\(d\\) \u2014 ikinci binomun iki terimi<\/li>\n<\/ul>\n<p>D\u00f6rt \u00e7arp\u0131m, FOIL harflerine kar\u015f\u0131l\u0131k gelir:<\/p>\n<ul>\n<li><strong>F<\/strong>irst (\u0130lk): \\(a \\cdot c\\) \u2014 her binomun ilk terimleri<\/li>\n<li><strong>O<\/strong>uter (D\u0131\u015f): \\(a \\cdot d\\) \u2014 en d\u0131\u015ftaki terimler<\/li>\n<li><strong>I<\/strong>nner (\u0130\u00e7): \\(b \\cdot c\\) \u2014 en i\u00e7teki terimler<\/li>\n<li><strong>L<\/strong>ast (Son): \\(b \\cdot d\\) \u2014 her binomun son terimleri<\/li>\n<\/ul>\n<p>\u00c7arpma i\u015fleminden sonra sadele\u015ftirilmi\u015f ifadeyi elde etmek i\u00e7in benzer terimleri \u2014 genellikle D\u0131\u015f ve \u0130\u00e7 \u00e7arp\u0131mlar\u0131n\u0131 \u2014 birle\u015ftirin.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.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 Hesaplama \u00d6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> \\((x + 2)(x + 3)\\) ifadesini FOIL y\u00f6ntemiyle a\u00e7\u0131n.<\/p>\n<p>\\[ \\text{\u0130lk (First): } x \\cdot x = x^2 \\]&lt;\/n<\/p>\n<p>\\[ \\text{D\u0131\u015f (Outer): } x \\cdot 3 = 3x \\]<\/p>\n<p>\\[ \\text{\u0130\u00e7 (Inner): } 2 \\cdot x = 2x \\]<\/p>\n<p>\\[ \\text{Son (Last): } 2 \\cdot 3 = 6 \\]<\/p>\n<p>Benzer terimler olan \\(3x\\) ve \\(2x\\)'i birle\u015ftirin:<\/p>\n<p>\\[ x^2 + 3x + 2x + 6 = x^2 + 5x + 6 \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> \\(x^2 + 5x + 6\\)<\/p>\n<p>\n\r\n<\/section>\n<h2>FOIL Hesaplama Arac\u0131 Nas\u0131l Kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li>\u0130lk binomu <strong>\u0130lk binom (a + b)<\/strong> alan\u0131na yaz\u0131n, \u00f6rne\u011fin <code>x + 2<\/code> veya <code>3x - 5<\/code>.<\/li>\n<li>\u0130kinci binomu <strong>\u0130kinci binom (c + d)<\/strong> alan\u0131na yaz\u0131n, \u00f6rne\u011fin <code>x + 3<\/code> veya <code>2x - 4<\/code>.<\/li>\n<li>Her iki binomun ayn\u0131 de\u011fi\u015fken harfini kulland\u0131\u011f\u0131ndan emin olun.<\/li>\n<li><strong>A\u00e7\u0131lm\u0131\u015f ifade<\/strong> alan\u0131 otomatik olarak g\u00fcncellenir ve sadele\u015ftirilmi\u015f \u00e7arp\u0131m\u0131 g\u00f6sterir.<\/li>\n<\/ol>\n<h2>FOIL Y\u00f6ntemi Nedir?<\/h2>\n<p>FOIL, <strong>First, Outer, Inner, Last<\/strong> (\u0130lk, D\u0131\u015f, \u0130\u00e7, Son) kelimelerinin bir hat\u0131rlatma kal\u0131b\u0131d\u0131r; iki binomun \u00e7arp\u0131m\u0131n\u0131 a\u00e7arken terimlerin hangi s\u0131rayla \u00e7arp\u0131laca\u011f\u0131n\u0131 g\u00f6sterir. Bu, da\u011f\u0131lma \u00f6zelli\u011fini iki kez uygulamak i\u00e7in d\u00fczenli bir yoldur:<\/p>\n<p>\\[ (a + b)(c + d) = a(c + d) + b(c + d) = ac + ad + bc + bd \\]<\/p>\n<p>Binomlar\u0131n \u00e7arp\u0131m\u0131 cebirin her yerinde kar\u015f\u0131m\u0131za \u00e7\u0131kar: ikinci derece ifadeler bu yolla olu\u015fur, denklemler \u00e7\u00f6z\u00fclmeden \u00f6nce bu yolla yeniden yaz\u0131l\u0131r ve bir\u00e7ok \u00e7arpanlara ay\u0131rma problemi bu i\u015flemin tersidir. \u00d6rne\u011fin, \\(x^2 + 5x + 6\\) ifadesi \u00e7arpanlara \\((x + 2)(x + 3)\\) \u015feklinde ayr\u0131l\u0131r ve FOIL, b\u00f6yle bir \u00e7arpanlara ay\u0131rmay\u0131 do\u011frulaman\u0131n en h\u0131zl\u0131 yoludur.<\/p>\n<p>\u0130ki lineer binoma FOIL uyguland\u0131\u011f\u0131nda sonu\u00e7 daima \\(Ax^2 + Bx + C\\) bi\u00e7iminde bir ikinci derece ifade olur. Orta katsay\u0131 \\(B\\), D\u0131\u015f ve \u0130\u00e7 \u00e7arp\u0131mlar\u0131n toplam\u0131d\u0131r \u2014 ikinci derece bir ifadeyi inceleme yoluyla \u00e7arpanlara ay\u0131r\u0131rken arad\u0131\u011f\u0131n\u0131z \u015fey tam olarak bu toplamd\u0131r. Ard\u0131ndan \\(Ax^2 + Bx + C = 0\\) denklemini \u00e7\u00f6zmeniz gerekirse, <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/ikinci-derece-denklem-cozucu\/\">\u0130kinci Derece Denklem Hesaplama Arac\u0131<\/a> veya <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/ikinci-derece-denklem-diskriminant\/\">\u0130kinci Derece Denklemin Diskriminant\u0131 Hesaplama Arac\u0131<\/a> i\u015fi oradan devralabilir.<\/p>\n<h2>Varsay\u0131mlar, S\u0131n\u0131rlamalar ve \u0130pu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>Yaln\u0131zca iki binom.<\/strong> FOIL, her biri iki terimli iki ifadenin \u00e7arp\u0131mlar\u0131 i\u00e7in ge\u00e7erlidir, \u00f6rne\u011fin \\((2x - 1)(x + 4)\\). Daha uzun polinomlar i\u00e7in tekrarl\u0131 da\u011f\u0131tma i\u015flemini veya genel bir <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/binom-carpimi\/\">Binom \u00c7arpma Hesaplama Arac\u0131<\/a>'n\u0131 ba\u015flang\u0131\u00e7 noktas\u0131 olarak kullan\u0131n, sonra terim terim da\u011f\u0131t\u0131n.<\/li>\n<li><strong>Ayn\u0131 de\u011fi\u015fken gerekir.<\/strong> Bu hesaplama arac\u0131, her iki binomun ayn\u0131 harfi kullanmas\u0131n\u0131 bekler, \u00f6rne\u011fin ikisi de \\(x\\) cinsinden. \\(x + 2\\) ve \\(y + 3\\) gibi de\u011fi\u015fkenlerin kar\u0131\u015ft\u0131r\u0131lmas\u0131 hata verecektir.<\/li>\n<li><strong>Kabul edilen bi\u00e7imler.<\/strong> Terimleri a\u00e7\u0131k katsay\u0131 ile (<code>3x<\/code>), 1'e e\u015fit \u00f6rt\u00fck katsay\u0131 ile (<code>x<\/code>) veya yaln\u0131zca sabit olarak girin. \u00c7\u0131karma i\u015flemi eksi i\u015faretiyle yaz\u0131l\u0131r, \u00f6rne\u011fin <code>3x - 5<\/code>.<\/li>\n<li><strong>\u0130\u015faretlere dikkat edin.<\/strong> Her iki binom da \u00e7\u0131karma i\u00e7erdi\u011finde, D\u0131\u015f ve \u0130\u00e7 \u00e7arp\u0131mlar negatiftir. \u00d6rne\u011fin, \\((x - 2)(x - 3) = x^2 - 3x - 2x + 6 = x^2 - 5x + 6\\).<\/li>\n<li><strong>Benzer terimleri birle\u015ftirin.<\/strong> Ham FOIL \u00e7\u0131kt\u0131s\u0131nda d\u00f6rt terim vard\u0131r; sadele\u015ftirmek i\u00e7in daima D\u0131\u015f ve \u0130\u00e7 \u00e7arp\u0131mlar\u0131 (ortadaki iki terim) toplay\u0131n. Bu hesaplama arac\u0131 bu ad\u0131m\u0131 sizin yerinize yapar.<\/li>\n<li><strong>\u00d6zel kal\u0131plar.<\/strong> \\((x + a)^2\\) gibi \u00e7arp\u0131mlar tam kare \u00fc\u00e7l\u00fcs\u00fc verir ve \\((a + b)(a - b)\\) \u00e7arp\u0131m\u0131, orta terimlerin birbirini g\u00f6t\u00fcrd\u00fc\u011f\u00fc kareler fark\u0131 verir \u2014 cevab\u0131n\u0131z\u0131 kontrol ederken tan\u0131maya de\u011fer pratik k\u0131sayollard\u0131r.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>FOIL y\u00f6ntemi (First, Outer, Inner, Last \u2014 \u0130lk, D\u0131\u015f, \u0130\u00e7, Son) ile iki binomun \u00e7arp\u0131m\u0131n\u0131 a\u00e7\u0131n. x + 2 ve x + 3 gibi ifadeleri girin ve sadele\u015ftirilmi\u015f ikinci derece sonucu an\u0131nda al\u0131n.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[16],"class_list":["post-365","post","type-post","status-publish","format-standard","hentry","category-matematik","tag-cebir"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/365","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=365"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/365\/revisions"}],"predecessor-version":[{"id":3001,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/365\/revisions\/3001"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=365"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=365"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=365"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}