MHB How to Write a Polynomial in Standard Form with Three Variables?

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To write a polynomial in standard form with three variables x, y, and z, it is essential to arrange the terms in descending order of their total degree. The standard form can be expressed as P(x,y,z) = a_n (xyz)^n + a_{n-1}(xyz)^{n-1} + ... + a_1 xyz + a_0, where each term is a product of coefficients and variables raised to non-negative integer powers. The coefficients a_n, a_{n-1}, ..., a_0 are real or complex numbers. Clarity in the arrangement of terms is crucial for proper interpretation and manipulation of the polynomial. Understanding this structure is fundamental for working with polynomials in multiple variables.
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how do you write a polynomial in three variables say x,y,z in standard form?
 
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The question is somehow vague , is this what you mean ?

$$P(x,y,z)= a_n (xyz)^n +a_{n-1}(xyz)^{n-1}+\cdots +a_1 xyz +a_0 $$
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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