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Algebra Difficulty 4.1 AIME Find the answer Philippines

Problem:
Find the sum of all (numerical) coefficients in the expansion of (x+y+z)3(x+y+z)^3.

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:

To find the sum of all numerical coefficients in the expansion of (x+y+z)3(x+y+z)^3, substitute x=1x=1, y=1y=1, z=1z=1:

(1+1+1)3=33=27.(1+1+1)^3 = 3^3 = 27.

Therefore, the sum of all coefficients is 2727.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.