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Öğretmen, 25. sorudan 33. soruya kadar olan problemleri adım adım çözmekte ve her bir çözüm için detaylı açıklamalar sunmaktadır."]},"endTime":1542,"title":"Matematik Dersi: Cebirsel İfadeler ve Çarpanlara Ayırma","beginTime":0}],"fullResult":[{"index":0,"title":"İki Küp Farkı ve Toplamı","list":{"type":"unordered","items":["İki küp toplamı formülü: x³ + y³ = (x + y)(x² - xy + y²)","İki küp farkı formülü: x³ - y³ = (x - y)(x² + xy + y²)","Fark formülünde, birinci ifadede artı varsa ikinci ifadede de artı, eksi varsa ikinci ifadede de eksi kullanılır."]},"beginTime":10,"endTime":42,"href":"/video/preview/16620025957075448233?parent-reqid=1774383509873687-10270996632474935114-balancer-l7leveler-kubr-yp-sas-57-BAL&text=Stay+Mathactive&t=10&ask_summarization=1"},{"index":1,"title":"Örneklerle İki Küp Farkı ve Toplamı","list":{"type":"unordered","items":["x³ + 27 = (x + 3)(x² - 3x + 9)","x³ - 8 = (x - 2)(x² + 2x + 4)","x³ + 1 = (x + 1)(x² - x + 1)","x³ - 64 = (x - 4)(x² + 4x + 16)","8x³ - 27 = (2x - 3)(4x² + 6x + 9)","x³/27 - y³ = (x/3 - y)(x²/9 + xy/3 + y²)"]},"beginTime":42,"endTime":192,"href":"/video/preview/16620025957075448233?parent-reqid=1774383509873687-10270996632474935114-balancer-l7leveler-kubr-yp-sas-57-BAL&text=Stay+Mathactive&t=42&ask_summarization=1"},{"index":2,"title":"Kesirlerde İki Küp Farkı ve Toplamı","list":{"type":"unordered","items":["(a³ + b³) / (a² - ab + b²) = (a + b) / (a² - ab + b²) = a + b (sadeleştirme)","(x³ + 1)³ / (x² - 1) = (x + 1)(x² - 2x + 1) / (x - 1)(x + 1) = (x² - x + 1) / (x - 1)"]},"beginTime":192,"endTime":317,"href":"/video/preview/16620025957075448233?parent-reqid=1774383509873687-10270996632474935114-balancer-l7leveler-kubr-yp-sas-57-BAL&text=Stay+Mathactive&t=192&ask_summarization=1"},{"index":3,"title":"Tam Küp İfadeler","list":{"type":"unordered","items":["(x + y)³ = x³ + 3x²y + 3xy² + y³ (toplama)","(x - y)³ = x³ - 3x²y + 3xy² - y³ (fark)","Tam küp ifadelerinde katsayılar 1, 3, 3, 1 şeklinde gider ve işaretler toplama durumunda artı, fark durumunda artı-eksi-artı-eksi şeklinde değişir."]},"beginTime":317,"endTime":549,"href":"/video/preview/16620025957075448233?parent-reqid=1774383509873687-10270996632474935114-balancer-l7leveler-kubr-yp-sas-57-BAL&text=Stay+Mathactive&t=317&ask_summarization=1"},{"index":4,"title":"Binom Açılımı","list":{"type":"unordered","items":["Binom açılımı formülü kullanılarak (x-1)³ ifadesi hesaplanıyor: x³ - 3x² + 3x - 1.","(2x+5)³ ifadesi hesaplanıyor: 8x³ - 60x² + 150xy² - 125y³."]},"beginTime":550,"endTime":668,"href":"/video/preview/16620025957075448233?parent-reqid=1774383509873687-10270996632474935114-balancer-l7leveler-kubr-yp-sas-57-BAL&text=Stay+Mathactive&t=550&ask_summarization=1"},{"index":5,"title":"Üç Terimli İfadelerin Çarpanlarına Ayrılması","list":{"type":"unordered","items":["x² katsayısı 1 olan üç terimli ifadelerin çarpanlarına ayrılması için sabit terimin çarpanları bulunur ve toplamları x'in katsayısına eşit olmalıdır.","Örnek olarak x²+5x+6 ifadesi (x+1)(x+5) şeklinde, x²-4x-5 ifadesi (x-1)(x-5) şeklinde çarpanlarına ayrılır.","Çarpanlara ayırma işlemi sırasında negatif terimlere de dikkat edilmelidir."]},"beginTime":668,"endTime":861,"href":"/video/preview/16620025957075448233?parent-reqid=1774383509873687-10270996632474935114-balancer-l7leveler-kubr-yp-sas-57-BAL&text=Stay+Mathactive&t=668&ask_summarization=1"},{"index":6,"title":"x² Katsayısı","list":{"type":"unordered","items":["x² katsayısı 1'den farklı olan üç terimli ifadelerin çarpanlarına ayrılması için önce x² katsayısının çarpanları bulunur.","Örneğin 2x²+5x+3 ifadesi (2x+3)(x+1) şeklinde çarpanlarına ayrılır.","Çarpanlara ayırma işlemi sırasında çarpımların toplamı ortadaki terimi vermelidir."]},"beginTime":861,"endTime":943,"href":"/video/preview/16620025957075448233?parent-reqid=1774383509873687-10270996632474935114-balancer-l7leveler-kubr-yp-sas-57-BAL&text=Stay+Mathactive&t=861&ask_summarization=1"},{"index":7,"title":"Çarpanlara Ayırma Örnekleri","list":{"type":"unordered","items":["2x²-3x-2 ifadesi (2x+1)(x-2) şeklinde çarpanlarına ayrılır.","10x²-15x-5 ifadesi (2x-5)(5x-1) şeklinde çarpanlarına ayrılır.","3x²-5x-2 ifadesi (3x+1)(x-2) şeklinde çarpanlarına ayrılır."]},"beginTime":943,"endTime":1105,"href":"/video/preview/16620025957075448233?parent-reqid=1774383509873687-10270996632474935114-balancer-l7leveler-kubr-yp-sas-57-BAL&text=Stay+Mathactive&t=943&ask_summarization=1"},{"index":8,"title":"Matematiksel İfadelerin Sadeleştirilmesi","list":{"type":"unordered","items":["x² - 2x ifadesi x parantezine alınarak x(x - 2) şeklinde yazılabilir.","x² - 4 ifadesi iki kare farkı olduğu için (x - 2)(x + 2) şeklinde yazılabilir.","Sadeleştirme işlemi sonucunda ifade x/(x + 2) şeklinde en sade haliyle bulunur."]},"beginTime":1107,"endTime":1146,"href":"/video/preview/16620025957075448233?parent-reqid=1774383509873687-10270996632474935114-balancer-l7leveler-kubr-yp-sas-57-BAL&text=Stay+Mathactive&t=1107&ask_summarization=1"},{"index":9,"title":"Ortak Çarpan Parantezine Alma","list":{"type":"unordered","items":["a(x - y) + 5(x - y) ifadesinde x - y ortak çarpan parantezine alınarak (x - y)(a + 5) şeklinde yazılabilir.","Payda da (a + 5) olduğu için sadeleştirme yapılarak ifade x - y olarak bulunur.","x² - 2x + 1 ifadesi (x - 1)² şeklinde yazılabilir ve sadeleştirme sonucunda x - 1/(x + 1) bulunur."]},"beginTime":1146,"endTime":1224,"href":"/video/preview/16620025957075448233?parent-reqid=1774383509873687-10270996632474935114-balancer-l7leveler-kubr-yp-sas-57-BAL&text=Stay+Mathactive&t=1146&ask_summarization=1"},{"index":10,"title":"Çarpanlara Ayırma ve Sadeleştirme","list":{"type":"unordered","items":["x² - 4 ifadesi (x - 5)(x + 1) şeklinde, x² - 1 ifadesi (x - 1)(x + 1) şeklinde yazılabilir.","x³ - 1 ifadesi (x - 1)(x² + x + 1) şeklinde yazılabilir.","x² - 4 ifadesi (x - 2)(x + 2) şeklinde, x² + 4 ifadesi (x + 2)² şeklinde yazılabilir."]},"beginTime":1224,"endTime":1327,"href":"/video/preview/16620025957075448233?parent-reqid=1774383509873687-10270996632474935114-balancer-l7leveler-kubr-yp-sas-57-BAL&text=Stay+Mathactive&t=1224&ask_summarization=1"},{"index":11,"title":"Karmaşık İfadelerin Sadeleştirilmesi","list":{"type":"unordered","items":["2x² + 5x + 2 ifadesi (2x + 1)(x + 2) şeklinde yazılabilir.","a³ - ab² ifadesi a²(a - b) şeklinde, a² - b² ifadesi (a - b)(a + b) şeklinde yazılabilir.","x² - 16 ifadesi (x - 4)(x + 4) şeklinde, x² + 4x ifadesi x(x + 4) şeklinde yazılabilir."]},"beginTime":1327,"endTime":1481,"href":"/video/preview/16620025957075448233?parent-reqid=1774383509873687-10270996632474935114-balancer-l7leveler-kubr-yp-sas-57-BAL&text=Stay+Mathactive&t=1327&ask_summarization=1"},{"index":12,"title":"Paydaları Eşitleme ve Sadeleştirme","list":{"type":"unordered","items":["1/a - 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