Vault Of Euclid

Coefficients in a Multinomial Expansion

Counting core

What is the coefficient of \(x^{99} y^{60} z^{14}\) in \((2x^3 + y - z^2)^{100}\)? What about \(x^{99} y^{61} z^{13}\)?

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What you need first

Binomial Theorem
Laws of exponents
Solving simple linear equations

What this problem tests

Tests the ability to apply the Multinomial Theorem and carefully match exponents to find specific coefficients.

This type of problem is common in introductory combinatorics and discrete mathematics courses.

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