Don’t Expand This! (The Multinomial Theorem) | HOW TO SOLVE | Combinatorics
Автор: The Pi Man
Загружено: 2026-01-23
Просмотров: 10
Описание:
If I asked you to expand (a+b)^{13}, you'd probably use Pascal's Triangle or the Binomial Theorem. But what happens when we add a third variable? Expanding (2x+y+3z)^{13} by hand would take hours and cover pages of paper.
In this video, I'll show you the power of the Multinomial Theorem—a generalized version of the Binomial Theorem that lets us pick out any specific coefficient instantly without expanding the whole equation.
The Problem:
Find the coefficient of the term x^2y^9z^2 in the expansion of (2x+y+3z)^{13}.
We will cover:
1. The difference between Binomial and Multinomial expansions.
2. The General Term formula (using factorials).
Timestamps:
0:00 - The "Impossible" Expansion
0:52 - Introducing the Multinomial Theorem
2:24 - Setting it up
4:30 - Final Calculation
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#MathOlympiad #Combinatorics #MultinomialTheorem #Algebra #MathTricks #CompetitonMath #STEM #maths #mathematics #math
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