Pascal’s Triangle & Binomial Theorem | Expansion, Patterns & Shortcuts - Pre-Calculus, Probability скачать в хорошем качестве

Pascal’s Triangle & Binomial Theorem | Expansion, Patterns & Shortcuts - Pre-Calculus, Probability

Take this quiz to check your level of mastery after watching the lesson : https://1drv.ms/w/c/2713457aa143ce7f/... In this lesson from the MathSupport channel, ‪@mathsupportnow‬ we explore the Binomial Theorem and its connection to Pascal’s Triangle. You’ll learn how to expand binomials, identify patterns in coefficients and exponents, and use shortcuts to find specific terms without full expansion. What You’ll Learn in This Video: ✅ What the Binomial Theorem is and how it expands (x + y)^n ✅ How Pascal’s Triangle generates coefficients for binomial expansions ✅ Why coefficients always start and end with 1, and follow addition patterns ✅ How exponents decrease for 𝑥 and increase for 𝑦 in expansions ✅ Why the number of terms in (𝑥+𝑦)^𝑛 is always 𝑛 + 1 ✅ How the sum of coefficients equals 2^𝑛 ✅ Step-by-step examples:    • Expanding • Using Pascal’s Triangle to expand • Shortcut for the Kth term in the expansion ✅ Historical context: Newton, Euler, Al-Khwarizmi, Jia Xian, and Pascal’s contributions 00:00 – Introduction: Pascal’s Triangle & Binomial Theorem 01:15 – Example: Expansion of (𝑥+𝑦)^4 02:00 – Coefficients & Patterns from Pascal’s Triangle 03:32 – Exponent Patterns: 𝑥 decreases, 𝑦 increases 06:08 – Building Pascal’s Triangle step by step 07:16 – Binomial Theorem explained with Pascal’s Triangle 08:28 – Example: Expanding (𝑥+𝑦)^5 10:05 – Number of terms & sum of coefficients = 2^𝑛 11:43 – Shortcut formula for the k-th term 12:26 – Example: Finding the 4th term 13:42 – Wrap-Up & Next Lesson Preview This video is ideal for : 🎯 Grade 9–12 Math (Canada, US, UK, Australia, IB, etc.) 🎯 Algebra, Combinatorics, or Pre-Calculus 🎯 Teachers, Tutors, Parents who need more resources 👍 Like if this helped you 🔔 Subscribe for more step-by-step math tutorials 💬 Comment with your questions or requests for future videos 📤 Share this with classmates, teachers, or study groups More Video lessons to review on combinatorics:    • Combinatorics Examples EASY STEP-BY-STEP s...      • The Famous Pathway Problem Explained | Pas...   #mathsupport #combinatorics #permutation #probability #mathhacks