【灘高入試】代数計算の最高峰。あなたは最後まで計算ミスせずに辿り着けるか？

[Nada High School 2003 Mathematics Entrance Exam Question] This video explains the algebraic calculation used to find the value of an algebraic expression from a Nada High School entrance exam question. At first glance, this problem appears to require a huge amount of calculation, but by focusing on the symmetry of the expression and making full use of factorization, it can be solved in a surprisingly orderly manner. This video focuses not only on the calculation steps, but also on the mathematical thought process of "why the transformation is performed." Whether you're a high school student or an adult looking to refresh your knowledge of mathematics, we encourage you to grab a pen and paper and give this a try. [Problem] x = √3 + √6 - 1/√3 - 1/√6 y = -√3 + √6 + 1/√3 - 1/√6 Find the value of x^3(2y - 1) + x^2y + xy^2(1 - 2y) - y^3 [Problem Solution] Factorize the desired expression First, rearrange the desired expression. x^3(2y - 1) + x^2y + xy^2(1 - 2y) - y^3 = 2x^3y - x^3 + x^2y + xy^2 - 2xy^3 - y^3 Let's rearrange this by combining terms. = (2x^3y - 2xy^3) - (x^3 - x^2y - xy^2 + y^3) = 2xy(x^2 - y^2) - {x^2(x - y) - y^2(x - y)} = 2xy(x - y)(x + y) - (x - y)(x^2 - y^2) = 2xy(x - y)(x + y) - (x - y)(x - y)(x + y) = (x - y)(x + y) {2xy - (x - y)} Reorganizing the x and y values: Notice that the given conditional expressions have many common terms. x + y = 2√6 - 2/√6 = 2√6 - √6/3 = 5√6/3 x - y = 2√3 - 2/√3 = 2√3 - 2√3/3 = 4√3/3 Calculating the product xy Since x = (√6 - 1/√6) + (√3 - 1/√3) and y = (√6 - 1/√6) - (√3 - 1/√3), this can be expressed as a product of the sum and difference (A^2 - B^2). xy = (√6 - 1/√6)^2 - (√3 - 1/√3)^2 = (6 - 2 + 1/6) - (3 - 2 + 1/3) = (4 + 1/6) - (1 + 1/3) = 25/6 - 4/3 = (25 - 8) / 6 = 17/6 Final calculation: (x + y)(x - y) = (5√6/3) * (4√3/3) = 20√18 / 9 = 60√2 / 9 = 20√2 / 3 Substitute these values ​​into the equation from step 1. 20√2/3 * {2 * 17/6 - 4√3/3} = 20√2/3 * {17/3 - 4√3/3} = 20√2(17 - 4√3) / 9 = (340√2 - 80√6) / 9 "Gaku Sensei's Arithmetic and Mathematics Class" shares the fun and essential concepts of mathematics through the entrance exams for prestigious schools. If you enjoy the channel, please subscribe and rate it. #NadaHigh #Mathematics #HighSchoolEntranceExam #JuniorHighSchoolEntranceExam #CalculationTips #Factorization #BrainTraining #GakuSensei #MathExplanation 🔗 Related Videos & Recommended Links [Junior High School Entrance Exam Math Problem Explanation Series] ▶    • 灘中入試問題 2005年度1日目｜素因数分解で分数の計算問題   [Junior High School Entrance Exam Integer Properties Practice Problems] ▶    • 【魔方陣の攻略法】真ん中の数の見つけ方！公務員試験＆中学受験の数的処理対策｜算数過去...   [Kaisei Junior High School Entrance Exam Questions & Past Paper Explanation Series] ▶    • 【開成中学の算数】単位分数の和と整数問題を徹底解説！2010年度過去問に挑戦｜中学受験算数   [Nada Junior High School Entrance Exam Questions and Past Exam Questions Explanation Series] ▶    • 灘中入試問題 2005年度1日目｜素因数分解で分数の計算問題   📢 A Request to Viewers If you found this video helpful, please let us know by "Like" or "Commenting"! We also welcome requests for questions you would like us to explain. 📌 About This Channel This channel provides fun ways to learn arithmetic and mathematics while steadily improving the skills needed for exams. We fully support everyone who wants to "improve their thinking skills" and "overcome their weaknesses"! 📩 Job Inquiries For interviews and job inquiries, please contact: 📧 [email protected] #JuniorHighSchoolEntranceExams #ExamMath #Mathematics