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fazlası için: https://www.khanacademy.org.tr Matematikten sanat tarihine, ekonomiden fen bilimlerine, basit toplamadan diferansiyel denklemlere, ilkokul seviyesinden üniversite seviyesine...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/1771199/6c1552b246e491e1c74a5a37d0bc5ada/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/1-x5GwEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"1","reqid":"1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=videoid:5230046273925311477","teaser":[{"list":{"type":"unordered","items":["Bu video, matematik eğitimi formatında bir ders anlatımıdır. Eğitmen, önceki videoda binom açılımını kullanarak a+b'nin dördüncü kuvvetini hesapladığını hatırlatarak, bu videoda Pascal üçgeni kullanarak aynı işlemi nasıl yapabileceğimizi göstermektedir.","Video, Pascal üçgeninin nasıl oluşturulacağını adım adım anlatarak başlıyor ve ardından a+b'nin dördüncü kuvvetinin Pascal üçgeni ile nasıl hesaplanacağını gösteriyor. Eğitmen, katsayıların nasıl elde edildiğini ve hangi terime ait olduğunu açıklıyor. Son olarak, Pascal üçgeninin binom açılımıyla nasıl ilişkili olduğunu, ilk üç kuvvet için (a+b)², (a+b)³ ve (a+b)⁴ örnekleri üzerinden detaylı şekilde anlatıyor."]},"endTime":392,"title":"Pascal Üçgeni ile Binom Açılımı","beginTime":0}],"fullResult":[{"index":0,"title":"Binom Açılımı ve Pascal Üçgeni","list":{"type":"unordered","items":["Önceki videoda (a+b)⁴'nin binom açılımı gösterilmişti, ancak daha büyük kuvvetler için daha kullanışlı olurdu.","Bu videoda Pascal üçgeni kullanılarak (a+b)⁴'nin açılımı hesaplanacak ve iki yöntem arasındaki ilişki incelenecek.","Pascal üçgeninde her terime kaç farklı yoldan ulaşılabileceği hesaplanarak katsayılar elde edilecek."]},"beginTime":0,"endTime":46,"href":"/video/preview/5230046273925311477?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=0&ask_summarization=1"},{"index":1,"title":"Pascal Üçgeninin Oluşturulması","list":{"type":"unordered","items":["Pascal üçgeni sıfırıncı kuvvetten başlayarak oluşturulur ve her satırdaki her terime kaç farklı yoldan ulaşılabileceği hesaplanır.","Sıfırıncı satırda sadece bir yol, birinci satırda iki yol, ikinci satırda üç yol, üçüncü satırda dört yol, dördüncü satırda beş yol ve beşinci satırda altı yol bulunur.","Bu sayılar binom katsayılarını oluşturur: 1, 4, 6, 4, 1."]},"beginTime":46,"endTime":196,"href":"/video/preview/5230046273925311477?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=46&ask_summarization=1"},{"index":2,"title":"Pascal Üçgeni ile Binom Açılımının Hesaplanması","list":{"type":"unordered","items":["Pascal üçgenindeki katsayılar kullanılarak (a+b)⁴'nin açılımı hesaplanır: a⁴ + 4a³b + 6ab² + 6ab + b⁴.","Pascal üçgeni, binom açılımında katsayıları ve terimleri doğru şekilde verir.","Pascal üçgeninin aynı sonucu vermesinin nedeni, her terimin elde edilme yollarının sayısından 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kombinasyonun yarısını alıp kombinasyon değerini çarpıp, kuvvetlerin farkını hesaplayarak bulunur.","Verilen ifadede toplam yedi terim olduğundan, ortadaki terim baştan dördüncü terimdir ve altının üçlü kombinasyonu ile hesaplanır.","Hesaplamalar sonucunda ortanca terim 540 a³b³ olarak bulunur."]},"beginTime":460,"endTime":526,"href":"/video/preview/8060994280472913059?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=460&ask_summarization=1"},{"index":7,"title":"Binom Açılımında Belirli Terimin Katsayısı","list":{"type":"unordered","items":["Binom açılımında belirli bir terimin katsayısını bulmak için, o terimin kuvvetini elde etmek için gerekli kombinasyon ve kuvvetlerin çarpımı hesaplanır.","Verilen ifadede x⁴'lü terimin katsayısı için x³ ve x² terimlerinin çarpımları incelenir.","Hesaplamalar sonucunda x⁴'lü terimin katsayısı 8 olarak bulunur."]},"beginTime":526,"endTime":635,"href":"/video/preview/8060994280472913059?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=526&ask_summarization=1"},{"index":8,"title":"Binom Açılımında Terim Eşitliği","list":{"type":"unordered","items":["Binom açılımında terim eşitliği için, aynı dereceli terimlerin katsayıları ve kuvvetleri birbirine eşit olmalıdır.","Verilen eşitlikte r=5 olarak bulunur ve bu değerle kombinasyon hesaplamaları yapılır.","Hesaplamalar sonucunda k değeri 12 olarak bulunur."]},"beginTime":635,"endTime":745,"href":"/video/preview/8060994280472913059?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=635&ask_summarization=1"},{"index":9,"title":"Kombinasyon Problemleri Çözümü","list":{"type":"unordered","items":["Bir kombinasyon probleminde, 11'in r'li kombinasyonu çarpı x üzeri 11-r çarpı y üzeri ifadesi a çarpı x üzeri be çarpı y üzeri 9'a eşitlenerek r=9 bulunur.","r=9 değeri yerine yazılıp, katsayılar eşitlenerek a=55 ve b=2 bulunur, toplamları 57 olur.","Sabit terim bulmak için 7'in r'li kombinasyonu çarpı (1/3) üzeri (7-r) çarpı (-2/2) üzeri r ifadesi kullanılır ve r=4 bulunur."]},"beginTime":750,"endTime":903,"href":"/video/preview/8060994280472913059?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=750&ask_summarization=1"},{"index":10,"title":"Sabit Terim Hesaplama","list":{"type":"unordered","items":["Sabit terim için 7'in 4'lü kombinasyonu çarpı (-1) üzeri 4 hesaplanır ve sonuç 560 olarak bulunur.","Bir bölü a üzeri 8'li terimin katsayısı 256 olduğunda, a'nın değeri 8 olarak bulunur.","a=8 değeri yerine yazılıp, katsayılar eşitlenerek x=12 olarak 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Sınıf Matematik İpucu Soru Bankası çözümü (ileri düzey, test 23) devam ediyor. Binom açılımında sabit terim nasıl...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3393373/aeec638f861fae76827a3a94285a27b9/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/HcSc4QEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"5","reqid":"1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=videoid:3019827601612731091","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik eğitmeni tarafından sunulan eğitim içeriğidir. Eğitmen, öğrencilere Pascal üçgeni ve binom açılımı konularında ileri düzey soruları çözmektedir.","Videoda toplam 11 farklı soru çözülmektedir. Sorular, binom açılımının katsayılar toplamı, sabit terim, terim sayısı ve belirli terimlerin bulunması gibi konuları içermektedir. Eğitmen, her soru için adım adım çözüm yöntemlerini göstermekte ve gerekli formülleri hatırlatmaktadır.","Özellikle binom açılımında terim bulma kuralı (n'in r'li kombinasyonu çarpı a üzeri n-r çarpı b üzeri n-r) detaylı olarak açıklanmakta ve sabit terim bulma yöntemi x'in kuvvetlerinin eşit olması gerektiği vurgulanarak anlatılmaktadır. Video, bir testin sonunda ve bir sonraki testte görüşmek üzere veda edilerek sona ermektedir."]},"endTime":908,"title":"Pascal Üçgeni ve Binom Açılımı İleri Düzey Soruları Çözümü","beginTime":0}],"fullResult":[{"index":0,"title":"Paskal Üçgeni ve Binom Açılımı Soruları","list":{"type":"unordered","items":["Video, Paskal üçgeni ve binom açılımı ile ilgili ileri düzey soruları çözmeye odaklanmaktadır.","Binom açılımında baştan r+1. terim hesaplanırken n'in r'li kombinasyonu çarpı a üzeri n-eksi-r çarpı b üzeri r formülü kullanılır.","Sondan r+1. terim hesaplanırken n'in r'li kombinasyonu çarpı a üzeri r çarpı b üzeri n-eksi-r formülü kullanılır."]},"beginTime":12,"endTime":45,"href":"/video/preview/3019827601612731091?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=12&ask_summarization=1"},{"index":1,"title":"İlk Soru Çözümü","list":{"type":"unordered","items":["(a+b)^n açılımında a'nın azalan kuvvetlerine göre açıldığında baştan altıncı terim ve sondan beşinci terim birbirine eşit olduğunda n=9 bulunur.","Katsayılar toplamı için a ve b'ye 1 yazılır, (1+1)^9 = 2^9 = 512 olarak hesaplanır."]},"beginTime":45,"endTime":154,"href":"/video/preview/3019827601612731091?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=45&ask_summarization=1"},{"index":2,"title":"İkinci Soru Çözümü","list":{"type":"unordered","items":["(3x-1)^n açılımında n=5 için sabit terim -1, n=4 için katsayılar toplamı 16 olarak hesaplanır.","Terim sayısı formülü n+1'dir, bu formül doğru olduğundan 2. ifade doğrudur."]},"beginTime":154,"endTime":205,"href":"/video/preview/3019827601612731091?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=154&ask_summarization=1"},{"index":3,"title":"Üçüncü Soru Çözümü","list":{"type":"unordered","items":["(x+5y-3)^5 açılımında x^5y^3 teriminin katsayısı hesaplanır.","Binom açılımı kullanılarak terimler yazılır ve katsayılar hesaplanır."]},"beginTime":205,"endTime":292,"href":"/video/preview/3019827601612731091?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=205&ask_summarization=1"},{"index":4,"title":"Dördüncü Soru Çözümü","list":{"type":"unordered","items":["(2x-3+1)^5 açılımında katsayılar toplamı 0, sabit terim 1 olarak hesaplanır.","Terim sayısı formülü (n+1)(n+2)/2'dir, bu formül kullanılarak 21 terim olduğu bulunur."]},"beginTime":292,"endTime":370,"href":"/video/preview/3019827601612731091?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=292&ask_summarization=1"},{"index":5,"title":"Beşinci ve Altıncı Soru Çözümü","list":{"type":"unordered","items":["(a^3+2a^2)^5 açılımında baştan üçüncü terim 40a^11 olarak hesaplanır.","(a^2-1/a^3)^7 açılımında baştan dördüncü terim -35/a olarak hesaplanır."]},"beginTime":370,"endTime":450,"href":"/video/preview/3019827601612731091?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=370&ask_summarization=1"},{"index":6,"title":"Yedinci Soru Çözümü","list":{"type":"unordered","items":["(a^2+an)^8 açılımında baştan dördüncü terimin katsayısı 448 olduğunda n=2 olarak bulunur."]},"beginTime":450,"endTime":509,"href":"/video/preview/3019827601612731091?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=450&ask_summarization=1"},{"index":7,"title":"Sekizinci Soru Çözümü","list":{"type":"unordered","items":["(a^2-2/a)^8 açılımındaki sabit terim 42.120 olarak hesaplanır."]},"beginTime":509,"endTime":590,"href":"/video/preview/3019827601612731091?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=509&ask_summarization=1"},{"index":8,"title":"Dokuzuncu ve Onuncu Soru Çözümü","list":{"type":"unordered","items":["(x^2+1/x^3)^n açılımında baştan beşinci terim sabit olduğunda n=10 olarak bulunur.","(2x-1)^7 açılımında x^3 teriminin katsayısı 280 olarak hesaplanır."]},"beginTime":590,"endTime":719,"href":"/video/preview/3019827601612731091?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=590&ask_summarization=1"},{"index":9,"title":"Sabit Terim Bulma","list":{"type":"unordered","items":["Sabit terim için x ifadelerinin ifadede olmaması gerekir ve ilk ifadelerin tamamen sadeleşmesi gerekir.","Sabit terim bulmak için x'in kuvvetleri birbirine eşit olmalıdır, örneğin 21-3 = 4 denkleminin çözümü r=3 olarak bulunur.","Sabit terim hesaplanırken kombinasyonlar ve kuvvetler hesaplanır, sonucunda -140 değerine eşitlik 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Eğitmen, terim sayısı hesaplama, sabit terim bulma, katsayılar toplamı hesaplama ve binom açılımının eşiti gibi konuları ele almaktadır. Her soru için adım adım çözüm yöntemi gösterilmekte ve gerekli formüller açıklanmaktadır. Video, 12 sorunun çözümüyle tamamlanmakta ve bir sonraki testte görüşmek üzere veda edilmektedir."]},"endTime":649,"title":"Pascal Üçgeni ve Binom Açılımı Orta Düzey Soruları Çözümü","beginTime":0}],"fullResult":[{"index":0,"title":"Pascal Üçgeni ve Binom Açılımı Soruları","list":{"type":"unordered","items":["Video, Pascal üçgeni ve binom açılımı ile ilgili orta düzey soruları çözecektir.","Kutunun üst kapağına yapılacak süslemede kullanılacak düğüm sayısı, ifadenin açılımlarındaki terim sayısı kadardır.","Binom açılımında baştan ve artı bir terim hesaplanırken n'in r'li kombinasyonu çarpı x üzeri n eksi r çarpı y üzeri r formülü kullanılır."]},"beginTime":12,"endTime":44,"href":"/video/preview/2211165669299094032?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=12&ask_summarization=1"},{"index":1,"title":"Sabit Terim ve Katsayılar Toplamı","list":{"type":"unordered","items":["Sabit terim bulmak için x'in kuvveti sıfır olmalıdır.","Katsayılar toplamını bulmak için değişken yerine bir yazılır.","Binom açılımında terim sayısı, kuvvetin bir fazlasına eşittir."]},"beginTime":44,"endTime":153,"href":"/video/preview/2211165669299094032?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=44&ask_summarization=1"},{"index":2,"title":"Örnek Sorular ve Çözümleri","list":{"type":"unordered","items":["Katsayılar toplamı bulmak için değişken yerine bir yazılır.","Sabit terim bulmak için x'in kuvveti sıfır olmalıdır.","Binom açılımında terim sayısı, kuvvetin bir fazlasına eşittir."]},"beginTime":153,"endTime":245,"href":"/video/preview/2211165669299094032?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=153&ask_summarization=1"},{"index":3,"title":"Karmaşık Binom Açılımları","list":{"type":"unordered","items":["Binom açılımlarında terimlerin katsayıları toplamı, değişken yerine bir yazarak bulunabilir.","Çift kuvvetli ifadelerde, tabanlar eşit olmalıdır.","Sabit terim bulmak için x'in kuvveti sıfır olmalıdır."]},"beginTime":245,"endTime":470,"href":"/video/preview/2211165669299094032?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=245&ask_summarization=1"},{"index":4,"title":"Son Örnekler","list":{"type":"unordered","items":["Binom açılımında terim sayısı, kuvvetin bir fazlasına eşittir.","Katsayılar toplamı bulmak için değişken yerine bir yazılır.","Binom açılımında terim sayısı, kuvvetin bir fazlasına eşittir."]},"beginTime":470,"endTime":623,"href":"/video/preview/2211165669299094032?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=470&ask_summarization=1"}],"linkTemplate":"/video/preview/2211165669299094032?parent-reqid=1767396412794508-8248465404147429818-balancer-l7leveler-kubr-yp-sas-122-BAL&text=Pascal+Hintablian&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Pascal Üçgeni ve Binom Açılımı Soru Çözümü | 10. 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