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

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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

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