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The Multinomial Theorem

Published online by Cambridge University Press:  03 November 2016

D. W. Bolton
D. W. Bolton*
Affiliation:
Sir Joseph Williamson's Mathematical School, Rochester
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Extract

As the name suggests, the Multinomial Theorem is an extension of the Binomial theorem, and it was when I first met the latter that I began to consider the trinomial and the possibility of a corresponding Pascal's triangle.

My mathematics master suggested that I construct the triangle myself. It became apparent that such a triangle may not be drawn, as the result is a pyramid or a tetrahedron where the apexes of the tetrahedron are occupied by the coefficients of xn, yn, zn in the expansion of (x + y + z)n.

This may be shown by forming expansion coefficient triangles for a trinomial of power 0, 1, 2, 3.

Type
Research Article
Information
The Mathematical Gazette , Volume 52 , Issue 382 , December 1968 , pp. 336 - 342
Copyright
Copyright © Mathematical Association 1968

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