Çarpanlara Ayırma -2 (Toplam Kare ve Fark Kare) | Matematik | Hocalara Geldik
512bin512 bin izleme
Yayın tarihi 16 mayıs 201516 mayıs 2015
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Öğretmen ve öğrenciler arasında diyaloglar geçmektedir.","Video, çarpanlara ayırma konusunu detaylı şekilde ele almaktadır. İlk bölümde toplam kare fark kare çarpanlara ayırma yöntemi, (a+b)² ve (a-b)² ifadelerinin formülleri ve çeşitli örnekler üzerinden anlatılmaktadır. 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Öğretmen ve öğrenciler arasında diyaloglar geçmektedir.","Video, çarpanlara ayırma konusunu detaylı şekilde ele almaktadır. İlk bölümde toplam kare fark kare çarpanlara ayırma yöntemi, (a+b)² ve (a-b)² ifadelerinin formülleri ve çeşitli örnekler üzerinden anlatılmaktadır. İkinci bölümde ise cebirsel ifadelerin çözümü, kare alma, iki kare farkı ve üç terimli ifadelerin karesi gibi konular işlenmektedir.","Videoda sayısal değerler, rasyonel sayılar ve karmaşık ifadelerin çarpanlara ayrılması, tam kare ifadelerin kök dışına çıkarılması, x, y, z gibi değişkenlerin değerlerini bulma ve ifadelerin en küçük değerini hesaplama gibi çeşitli teknikler örneklerle açıklanmaktadır."]},"endTime":1243,"title":"Matematik Dersi: Çarpanlara Ayırma Teknikleri","beginTime":0}],"fullResult":[{"index":0,"title":"Toplam ve Fark Karesi Formülleri","list":{"type":"unordered","items":["Toplam kare formülü (a+b)² = a² + 2ab + b² olarak hesaplanır ve sözel olarak \"birincinin karesi, birinci ile ikincinin çarpımının iki katı, artı ikincinin karesi\" şeklinde ifade edilir.","Fark kare formülü (a-b)² = a² - 2ab + b² olarak hesaplanır ve toplam kare formülüyle benzerdir, sadece ikinci terimde işaret farklıdır.","Örnek olarak (2x+3y)² = 4x² + 12xy + 9y² ve (2x-1)² = 4x² - 4x + 1 şeklinde hesaplanır."]},"beginTime":0,"endTime":113,"href":"/video/preview/17405120468210759286?parent-reqid=1752665115435293-826552319258731758-balancer-l7leveler-kubr-yp-vla-201-BAL&text=Semka+Kare&t=0&ask_summarization=1"},{"index":1,"title":"Toplam ve Fark Karesi Uygulamaları","list":{"type":"unordered","items":["a²+b²=13 ve ab=6 verildiğinde, (a+b)²=25 ve (a-b)²=1 olur, bu da a+b=±5 ve a-b=±1 sonucunu verir.","49²+102 ifadesi 49²+2×49×51+51² şeklinde yazılabilir ve (49+51)²=100²=10100 şeklinde hesaplanır.","a²+6a+4=27 ifadesinde, (a+3)²=36 şeklinde yazılabilir ve a+3=±6 sonucu elde edilir."]},"beginTime":113,"endTime":337,"href":"/video/preview/17405120468210759286?parent-reqid=1752665115435293-826552319258731758-balancer-l7leveler-kubr-yp-vla-201-BAL&text=Semka+Kare&t=113&ask_summarization=1"},{"index":2,"title":"Karmaşık Soru Çözümleri","list":{"type":"unordered","items":["x+1/x=5 olduğunda, her iki tarafın karesini alarak x²+1/x²=23 sonucuna ulaşılır.","(a+b)²=a²+b²+2ab formülünden yararlanarak, (a+b)²=(a-b)²+4ab ilişkisi kurulabilir.","x²-1/x² ifadesi, (x-1/x)(x+1/x) şeklinde yazılabilir ve x-1/x=±√21 sonucuna ulaşılır."]},"beginTime":337,"endTime":472,"href":"/video/preview/17405120468210759286?parent-reqid=1752665115435293-826552319258731758-balancer-l7leveler-kubr-yp-vla-201-BAL&text=Semka+Kare&t=337&ask_summarization=1"},{"index":3,"title":"Köklü İfadelerin Çözümü","list":{"type":"unordered","items":["256=2¹⁰ ifadesi 2⁵² şeklinde yazılabilir ve √(256+256×2+1) ifadesi √(2⁵+1)²=2⁵+1=33 şeklinde çözülür.","Köklü ifadelerde tam kareleri tespit etmek önemlidir, örneğin √(4/9+20/21+25/49) ifadesi √((2/3+5/7)²) şeklinde yazılabilir.","Kök dışına çıkarken mutlak değer kullanmak gerekir, örneğin √((2/3-5/7)²)=|2/3-5/7| şeklinde 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